Fate plays an enormous role in Romeo and Juliet. In fact, it's almost like a character in its own right. Fate has conspired to ensure that that Romeo and Juliet, these two young people from warring families will meet, fall in love, and get married.

Sadly, fate is also responsible for their deaths. At one point in the play, Romeo expresses his exasperation at being “fortune's fool”, implying strongly that he is the mere plaything of fate. How else to account for his extraordinary bad luck, whose latest manifestation is his killing of Tybalt in a duel?

And in the Prologue, Romeo and Juliet are described as “star-crossed lovers,” meaning that the stars are working against them and their love. In Shakespeare's day, it was widely believed that the course of one's life was determined by the position and movement of the stars. Astrology was very popular at that time, and people would often consult astrologers in the hope of finding out what fate had set down for them by the stars.

We don't need an astrologer to tell us what fate lies in store for Romeo and Juliet; it's all there in the Prologue. The line “a pair of star-crossed lovers take their life” indicates, furthermore, that the precise manner of their deaths was also fated.

In the prologue that precedes act 1 the audience is straight away made aware that fate will play a huge role in the play. We are told that "from forth the fatal loins" of the Capulets and Montagues there is born "a pair of star-crossed lovers." The word "fatal" has two meanings here. First, it suggests death, and second, it suggests fate. The implication is that from these two families there has been born two people who were fated to become "lovers" but also fated to die. These lovers are also described as "star-crossed," which again implies that they were fated to love one another. At this time, in the Jacobean period, many people believed that one's fate was determined by the position of the stars on the day of one's birth.

In act 3, scene 5, when Juliet is watching Romeo climb down from her balcony, she imagines that she sees Romeo "as one dead in the bottom of a tomb." This vision is one of several indications that fate will not allow Romeo and Juliet to be together for very long. Juliet's vision is indeed prophetic, as this is the last time she will ever see Romeo alive.

Another indication in the play that Romeo and Juliet's relationship is fated to end in tragedy can be found when Friar Laurence compares their relationship to "fire and powder." In act 2, scene 6, for example, Friar Laurence warns Romeo and Juliet that their love is "like fire and powder." The image conveyed here is of a lit trail of gunpowder. The audience can imagine for themselves the inevitable explosion at the end of that trail. This image serves to remind the audience that just as a lit trail of gunpowder will inevitably end with an explosion, so too will Romeo and Juliet's relationship end in tragedy.

Fate, or the belief that a power greater than man guides and controls the lives of men, plays a tremendous role in Romeo and Juliet, in fact, it is infused throughout the play, to the point that the characters are even aware of it, seeing omens in many situations.  Fate works in all aspects of the lovers’ relationship from start with Romeo falling instantly in love with Juliet at a party he never should have attended in an attempt to see another girl.  Juliet is the daughter of the enemy of his family, yet love blooms instantly in spite of the feud; here is an excellent example of fate intervening in the relationship.  Romeo pursues Juliet quickly and relentlessly, driven by love (or lust whichever is more likely in a teenage boy of his age) to propose marriage, and Friar Laurence’s reluctant agreement to perform the ceremony, once again demonstrate fate.  Perhaps the saddest, yet best example of fate in the drama occurs at the end when Romeo misses Balthasar, who carries news of Friar Laurence’s plan and Juliet’s feigned death, only to arrive and kill himself in a cruel twist of fate because he thinks she is dead only moments before she awakens and kills herself because he is now dead.  The whole play is one huge example of how cruel fate can be and how events, small and large, work together to make or break any given event, even a potentially great love, such as that of Romeo and Juliet.  Maybe it all happened to teach the feuding families a lesson. 

Well you could say that fate played a very big role in Romeo and Juliet. It was fate that Romeo decided to crash Juliet's party and that she was the woman he fell in love with. SHakespeare plays with the idea of fate/fortune and how it ultimatly rules one. This is obvious in this quote, that Juliet says after Romeo leaves. In the end, she is saying, everything is left up to fortune.

"O fortune, fortune! all men call thee fickle:
If thou art fickle, what dost thou with him
That is renown'd for faith? Be fickle, fortune;
For then, I hope, thou wilt not keep him long
But send him back"
(V, ii)

Perhaps "fate" is contrasted with "faith" to reveal something about the nature of the love between Romeo and Juliet. As Jamie notes, Juliet addresses fate, or fortune asking for help:

O Fortune, Fortune, all men call thee fickle;
If thou art fickle, what dost thou with him
That is renown'd for faith? Be fickle, Fortune:
For then I hope thou wilt not keep him long,
But send him back.

I wonder whether an Elizabethan audience might see this as yet another example of misplaced faith. If Juliet had as much faith as her love, would she not request help from God or even Romeo's god, Love? This passage seems to suggest that she thinks Fate (and not Love) is in control of their lives. Perhaps in devoting themselves to one another, and making each other the gods of their idolatry, they have become pagan and subject to pagan gods and pagan rules (one of which is that fickle fortune's wheel will turn).

If this is the case, then the "star-crossed lovers" are star-crossed in every sense of the word. Their love has blinded them and left them vulnerable.

References to "fortune" and the "stars" throughout the play see Romeo and Juliet as helpless victims of fate. The Prologue to Act I refers to them as "star-crossed lovers". Other examples include Romeo's inability to stop the fight between Mercutio and Tybalt and Friar John's delay in being able to get the Friar's message to Romeo. Even the way the couple meets could be considered fate. Romeo crashes the Capulet party to see Rosaline; instead, he meets and falls in love with Juliet.

Fate is one of the predominant themes of the play. As the analysis here at eNotes indicates, Shakespeare places relies heavily on the "Elizabethan concept of Fortune or Fate."

For example, "upon learning of Mercutio's death, Romeo exclaims, "This day's black fate on more days doth depend, / This but begins the woe others must end" (III.i.119-120). In Act III, scene v, Juliet addresses Fortune (or Fate) and implores its aid.

O Fortune, Fortune, all men call thee fickle;
If thou art fickle, what dost thou with him
That is renown'd for faith? Be fickle, Fortune:
For then I hope thou wilt not keep him long,
But send him back.
(ll.60-64).

Fortune (or fate) is fickle: it is improbable that so perfectly matched a couple should be barred by a senseless family conflict (the cause of which is never mentioned and cannot be recalled); it is only through mischance that Romeo takes his own life in the mistaken belief that his love is dead, causing her to follow suit."

How does fate, choice and chance impact on the tragedy of Romeo and Juliet?

Fate is the ultimate variable; we could argue that the young lovers are "fated" for disaster.  Their feuding families have a long history; both are young and hormonally influenced; neither has a strong parent to advise them; the priest they trust is inept at best, evil at worst. 

Chance and fate are not easily separated.  But by chance, Juliet bumps into Romeo who has crashed her parents' party.  Chance places Mercutio in the path of his, and Romeo's, rival; chance, or arguably, fate, causes the letter of explanation to Romeo regarding Friar Laurence's sleeping potion scheme to remain unknown. 

Choice is more easily understood.  The lovers make a clear choice to defy their parents' wishes.  The friar makes a choice to be strong-armed into Juliet's will (she threatens suicide); the Nurse also chooses to aid and abet the couple.  The list goes on and on. 

Quotes that illustrate "fate", chance", and "choice": 

Fate:  My only love, sprung from my only hate! / Too early seen unknown, and known too late! / Prodigious birth of love it is to me / That I must love a loathed enemy (I.5).

Chocie:  Deny thy father and refuse thy name. / Or if thou wilt not, be but sworn my love / And I'll no longer be a Capulet (2.2).

Chance:  But soft! What light through yonder window breaks?
It is the East, and Juliet is the sun! (2.2)

What is Romeo and Juliet's destiny in Romeo and Juliet?

Juliet's destiny is to die a tragic death by her own hand. We know this because it explicitly says so in the play's Prologue. It's all in the stars, apparently, an indication of the widespread belief in astrology that characterized the age in which the play was written.

What we don't yet know, of course, is how this all comes about and why. There's an awfully long way to go before we reach that heart-rending moment when a distraught Juliet will stab herself to death upon finding the corpse of her beloved Romeo. That gives Shakespeare plenty of time to devise a suitably intriguing and convoluted plot that brings the star-crossed lovers together forever, but only in death.

It's a measure of The Bard's considerable skills as a dramatist that we're emotionally invested in Romeo and Juliet, even though we know of their tragic fate. There always seems to be the faintest hope that maybe, just maybe, the two young love-birds will avoid their unhappy fate. That such hope exists at all is a testament to the immense skill with which Shakespeare draws his two main characters and of the rich, intriguing plot in which he embroils them.

What is Romeo and Juliet's destiny in Romeo and Juliet?

We learn in the Prologue to Romeo and Juliet, delivered by the Chorus, that the love affair that blossoms between the title characters will not end happily for them:

A pair of star-cross'd lovers take their life;
Whose misadventure's piteous overthrows
Doth, with their death, bury their parents’ strife.

"Star-cross'd" here means something more than "unlucky." It basically means that Romeo and Juliet are doomed to die by fate. So their destiny is to meet, to fall in love, and to die as a result of their love. At the same time, their deaths will "bury their parents' strife." In other words, the feuding Capulets and Montagues will be reconciled by their grief. It took the deaths of these two young lovers to make them realize how destructive their mutual hatred really was. 

Some might think that discovering that the two lovers are destined to die in the Prologue lessens the suspense of the play. But it also creates a sense of dramatic irony that is absolutely heartbreaking. Romeo and Juliet's love is tender, genuine, and eloquently expressed, and knowing that it is doomed makes their declarations of love and of hope all the more poignant. We know that they cannot escape their destiny, yet we find ourselves rooting for them until they meet their tragic end together.

How does Shakespeare explore the theme of fate in Romeo and Juliet?

Shakespeare's Romeo and Juliet opens with a prologue that details the subject of fate. In a description of the events to come, it is stated that:

From forth the fatal loins of these two foes

A pair of star-cross'd lovers take their life;

Whose misadventures piteous overthrows

Do with their death bury their parents' strife.

The particular use of the term "star-cross'd" suggests that Romeo and Juliet's relationship was doomed from the start—born, bred, and eventually killed off by the poor alignment of the stars or dismissive hand of fate. Is this true, though? Is fate responsible for the tragedy that occurs in this play, or are characters' impulsive actions and mistakes the source of their downfall? 

Shakespeare never gives us a concrete answer on the matter, but he certainly does reference fate frequently throughout the play. Prior to the Capulets' ball, Romeo states:

...my mind misgives

Some consequence yet hanging in the stars

Shall bitterly begin his fearful date

With this night's revels and expire the term

Of a despised life closed in my breast

By some vile forget of untimely death.

But He, that hath the steerage of my course,

Direct my sail! On, lusty gentleman.

Here, Romeo is predicting that the night ahead of them will be fateful, but not necessarily in a good way... rather, in a manner that ultimately will be resolved in death. Regardless, Romeo embraces his "fate," and fateful the night is; Romeo meets Juliet at this ball, which sets off the events of the remainder of the play.

Other references to fate are aplenty within the text. The metaphor of stars as guiding entities re-enters when Romeo describes Juliet's eyes as "two of the fairest stars in all the heaven." Within Juliet's eyes lie Romeo's fate. When Mercutio dies in a duel with Tybalt, Romeo exclaims, "This day's black fate on more days doth depend," which implies that, once again, another death was determined by fate. When Romeo falsely learns of Juliet's "death," he screams out, "I defy you, stars!"

Overall, Shakespeare explores the human tension between taking accountability for our actions and wanting to ascribe our problems to fate. While the characters within Romeo and Juliet often look to fate or the stars to deal with the losses they experience, they ultimately have to suffer the consequences of their actions on this earthly plane. 

Discuss the role of fate in Romeo and Juliet.

I'd like to add some comments to the fine answer above.

Shakespeare tells us in the Prologue to the play that

From forth the fatal loins of these two foes
A pair of star-cross'd lovers take their life;
Whose misadventured piteous overthrows
Do with their death bury their parents' strife,

implying that fate, using the metaphor of "star-cross'd lovers," destroys the two young lovers, but its worth considering that the hatred between the Montagues and Capulets and, by extension, the families themselves, are  the real culprits here.  We need to keep in mind that the hatred between these two families goes so far back in time that no one knows with certainty what started the all-consuming hatred.  It is as if the effect--the death of the two young lovers--is without an identifiable and, more important, justifiable cause.

Rather than view just Romeo and Juliet as "star-cross'd" victims, perhaps we must look to the Montagues and Capulets as cause and victim of this tragedy.  If fate is the cause of this tragedy, it is fate aided by the willing participants. In the closing moments of the play, Capulet says

As rich shall Romeo's by his lady's lie;
Poor sacrifices of our enmity.

Capulet cuts through the web of possible causes of this tragedy to its essence and origin--the framework of hatred that essentially dictates the outcome.  Fate itself has only a small part to play in a world in which Juliet and Romeo are caught in a web of family hatred that traps them securely.  Capulet recognizes that "our enmity" prevailed over the love that bound Romeo and Juliet.

The Prince's conclusion acknowledges that fate ("Heaven") had a role in this tragedy, but he assigns the real blame to Capulet and Montague:

Where be these enemies? Capulet! Montague!
See, what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love

Clearly, the "scourge" of the families' hatred is the prime mover of the tragedy.  Fate itself is an interested by-stander.

Discuss the role of fate in Romeo and Juliet.

The Prologue to the play reminds the audience that Fate is central in ROMEO & JULIET.  Though the characters seem to control their own lives through their bold, rash, and romantic actions, fate steers them toward a foretold outcome.  Of course, Romeo and Juliet do not know their fate in the way that the audience does.  But, we willingly suspend our insight into the plays dramatic irony.  In the audience, we hope against hope that Romeo and Juliet can outrun, outwit, or 'outlive' their predetermined fate.  We know they can't, but Shakespeare knows that we will cheer on the young lovers' attempts to control their lives because we too hope to avoid our own mortality, our own limitations, and our own fates.  For a while, it seems that Romeo and Juliet will succeed in their desperate, impassioned attempt to outrun fate.  The play lures us into believing that these crazy kids can beat all odds and make it.  Our belief in Romeo and Juliet, and our hopes for them, are the plays central manipulation of its audience.  Of course Romeo and Juliet can't escape their fate. Nobody can.  We can't.  We know it.  But, it sure is fun to pretend that we can escape fate -- as if impossibly pure love will convince Fate to grant just this one pardon.  The play's Prologue reminds us that attempts at escape fate are futile for the characters and for us.  Shakespeare knows that he has warned us, and he knows that if his play works, we will forget his warnings by Act IV and remember them with some sense of knowing shame by the end of Act V.

What is the role of destiny in Shakespeare's Romeo and Juliet?

As early as the Prologue, the audience learns that the lovers have sprung from the "fatal loins of [...] two foes"; fatal, here, means fateful: thus, they are all involved in a destiny from which they cannot deviate.  Further, Romeo and Juliet are described as "star-crossed lovers," meaning that they are destined to be terribly unlucky in love (6).  

Romeo is the first of the pair to have some inkling of this.  On the night of the Capulets' party, as he has just become convinced to accompany his friends, he says,

my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night's revels, and expire the term
Of a despised life closed in my breast
By some vile forfeit of untimely death. (1.4.113-118)

He seems to intuitively understand that, by going to the party, he will set into motion some kind of fated plan; again the reference to the stars indicates destiny: something predetermined.  This party initiates his fate, and he prophesies that it will end with his too-soon death.  Such ability to prophesy is most often connected with the idea that we each have a destiny which we cannot help but fulfill.  

After slaying Tybalt in rage over Tybalt's slaying of his friend, Mercutio, Romeo cries, "O, I am Fortune's fool!" (3.1.142).  By this, he means that he feels like the plaything, or something meant to entertain, the goddess Fortuna who controls the fate or destiny of humans by spinning her wheel.  

Later, when Romeo leaves Juliet's bedroom, she says, "O God, I have an ill-divining soul! / Methinks I see thee, now thou art so low, / As one dead in the bottom of a tomb" (3.5.54-56).  In this moment, Juliet believes her soul has the ability to prophesy evil and that she is glimpsing something of their future.  Indeed, she is.  She will, later, wake up in her tomb to find Romeo dead beside her.  Such ability implies that destiny is in charge, despite all the lovers' attempts to thwart it.

Therefore, one could make the argument that destiny (or fate) plays a significant role in this play.  Certainly, if Romeo and Juliet were able to make plans or decisions not frustrated by events that were totally out of their control, it would be more difficult to make such an argument, but they are, clearly, met, time and time again, with awful, terrible luck.  The fact that they can only really be together in death seems to signify that "the stars" would simply never let them be together in life.

What are some of the powers of fate in the play Romeo and Juliet?

Romeo and Juliet have a destined love that is not meant to be. It is a love they cannot live with or without. It turns them upside down and inside out. It is simply Shakespeare when a destined love not meant to be finds destiny.

As fate would have it, Romeo attends the masqerade and finds Juliet. As fate would have it, she is a Capulet. As fate would have it, Romeo is Montague. As fate would have it, Romeo falls in love with a young girl he cannot have.

Fate again prevails when Romeo believes that his beloved Juliet is dead. As fate would have it, Romeo does not get word that Juliet is only sleeping. As fate would have it, Juliet wakes up and finds Romeo dead. As fate would have have it, she kills herself.

As fate would have it, two deaths cause two families to reconcile. The Capulets and Montagues realize the price it has taken for them to realize how ridiculous and even dangerous their hatred has been.

What role does fate play in contributing to the deaths of Romeo and Juliet?

That is a really interesting discussion question because there isn't a single perfect answer.

The prologue to the play stresses the role of fate in the story. The lovers are "star-crossed" and come from "fatal loins." It would seem that Fate determines what happens in Verona. However, the prologue seems to have been added after the first stagings of the play, so it is a consequence rather than a prophecy of what will happen. It is also one of the three sonnets in the play, and sonnets are highly artificial poetic forms, identified or determined in part by rhyme scheme. Given the required rhyme scheme, "mutiny" and "dignity" or "scene" and unclean" are somewhat fated. The words have to sound alike and there are a fixed number of words that could fit those end spots. Similarly, Friar Lawrence who speaks in rhymed couplets tends to think in terms of limited possibilities. The aesthetic style of the play seems to lend a certain credence to things being "fated" but we know that in art, we can use other forms. This means we have to see "fate" as a product of Shakespeare as much as "the gods."

Within the play story itself, we might think that Romeo and Juliet were fated to fall in love at first sight. But Benvolio had primed Romeo to find a woman who would be more beautiful (and maybe more pliable) than Rosaline, the woman who has been rejecting Romeo. Juliet promised her mother to try to look with love on Paris, to allow desire to be awakened so that she would be ready for her arranged marriage. In that moment, both of these young lovers encounter each other and their willingness to love is mutually attractive.

Up until Mercutio dies, the play in fact seems like a pretty simple and silly romantic comedy, much in the style of A Midsummer Night's Dream. Mercutio's death seems more accident, or the product of too hot a day and too hot a temper among the young men. Chance more than fate seems to govern this death, and Romeo's unrestrained passion leads to Tybalt's death.

Similarly, it seems more like chance than fate that a plague prevented Friar Lawrence's letter from reaching Romeo, informing him of the plan to rescue Juliet from the crypt. And chance seems to be at work in the ill-timed series of events that lead to Romeo's and Juliet's suicides.

The question then would concern whether chance and fate, or luck and fate, are the same thing. If so, then who drives or ordains either? In a narrative like this, it's Shakespeare, who tweaks his source material just enough to intensify the element of time in his play (the original takes place over months). Shakespeare works out the plot and writes the play in such a way that things seem to have to happen in a fixed way, but he is also the one who writes the play in a way where we can wonder what is driving the tragic action and what it means. If these deaths are fated, we want them to mean something. If they are not, the play may be less tragic (and more about victims of bad luck or family pride) but then we likely feel less of a catharsis for the sorrowful feelings evoked by these deaths.

The common Renaissance trope of the creator as a divine-like person pertains here, but Shakespeare also seems to leave enough doubt or irony in his work that it still seems valuable to be questioning these elements centuries after he wrote the play.

What role does fate play in contributing to the deaths of Romeo and Juliet?

The Prologue to the play foreshadows the role fate will play in the death of the two lovers in the following lines:

From forth the fatal loins of these two foes

A pair of star-cross'd lovers take their life;

The phrase "fatal loins" suggests that the feud leading to the death of the two lovers, like the conflicts of Greek tragedy, was some sort of fate that was transferred down across generations. 

The phrase "star-crossed" refers specifically to astrology, a theory that one can discover people's fate by looking at the position of the stars at their birth. "Star-crossed" specifically means that the unfortunate fates of the two lovers were predestined and readable in their stars.

One sees this reflected in the plot, in the way that coincidences, accidents, and misunderstandings seem to conspire to keep the two lovers apart, suggesting that their relationship was indeed doomed by fate. 

How does the concept of fate/destiny manifest itself in the events of the play Romeo and Juliet?

It is a combination of fate, bad luck, and bad choices that leads to Romeo and Juliet's deaths, and the audience feels both annoyed with them and sorry for them.

The Prologue prepares us for the fact that Romeo and Juliet are going to fall in love and die.

From forth the fatal loins of these two foes(5)

A pair of star-cross'd lovers take their life;

Whose misadventur'd piteous overthrows

Doth, with their death, bury their parents’ strife.

By saying that they are “star-crossed,” Shakepeare is telling us that they fated to fall in love.  In that case, they had no choice.  The fact that their families were feuding is in some ways bad luck then. Did they find each other more attractive in spite of the family feud, or because of it? 

Is she a Capulet?(125)

O dear account! my life is my foe's debt. (Act 1, Scene 5)

There is no real way to tell.  We do know that when the lovers first meet, neither one knows who the other is.  Thus they were attracted to each other without knowing their love was forbidden, although it is possible that the forbidden love made the love stronger.

There are other instances in which fate or luck play a role.  The most notable of which is Romeo’s killing Tybalt.  This one event is the one on which all others turn and it was a complete accident.  Romeo never had any desire to take part in a fray.  He tried to intercede on Mercutio’s behalf and ended up getting him killed.  Then he had to fight Tybalt and ended up killing him.

Mercutio's soul

Is but a little way above our heads,

Staying for thine to keep him company.

Either thou or I, or both, must go with him. (Act 3, Scene 1)

 Romeo was banished, and he and Juliet had to get married in secret.  Juliet’s parents had no idea, so they wanted her to marry Paris.  You could argue that there is more than bad luck at play there.  If they had listened to their daughter when she said she did not want to get married, it would have saved her life.

Romeo finding Juliet still asleep because he didn’t get the note telling him she faked her death is another case of very bad luck.  When Juliet wakes up to find Romeo dead, and has time to kill herself, this is another terrible coincidence.

At the end of the play, the audience feels sorry for the lovers and the parents, but also feels that they all brought a lot of it down on themselves.

Explain the role fate plays in Romeo and Juliet and how it affects the course of action and characters' lives.

In many ways, fate seems to be the driving force in the play.  It is even referenced in the Prologue; after the Chorus describes the feud between the Capulets and Montagues, they say, "From forth the fatal loins of these two foes / A pair of star-crossed lovers take their life" (lines 5-6).  Thus, there was even something fateful ("fatal") in the births of Romeo and Juliet, and they are "star-crossed," or impeded by fate through the destructive influence of the stars.  Even from their births, then, they were destined to die; their relationship could be nothing but "misadventured" or unlucky (7).  

Later, when Romeo's friends are trying to convince him to go with them to crash the Capulets' party, he says that he fears some events that have not unfolded yet, and that -- by going to that party -- he will set into motion these events which will eventually "expire the term / Of a despised life closed in [his] breast / By some vile forfeit of untimely death" (1.4.116-118).  Romeo has a kind of premonition that going to Lord Capulet's home will be the action that initiates some consequences that will absolutely result in his own death.  However, he doesn't seem to think that he has much choice in the matter, as he says, "But he that hath the steerage of my course / Direct my sail" (1.4.119-120).  He does not feel that he actually controls his own life, as he feels compelled to take this action regardless of the fact that it will lead to his destruction.  

Even the way Romeo and Juliet compare one another to celestial bodies seems ill-fated.  He compares her to the sun when he sees her on her balcony, and she asks for him to be cut into little stars and placed in the sky after he dies.  

How does fate affect the tragedy which occurs in Romeo and Juliet?

From the very beginning in the Prologue, we are introduced to the theme of Fate as Romeo and Juliet are described as "a pair of star-crossd lovers" (Prologue, Romeo and Juliet).  The idea here is that the two are fated to meet and die together for their love which is misunderstood and may never be accepted by their feuding families. It is not so much that fate affects the tragedy as much as it is the cause for the tragedy.  This concept creates the idea that there was nothing Romeo and Juliet could do to avoid their fate, basically, each other. Because they were meant to meet, it was something that could not be avoided and really it is evident that the stars had to be aligned in some way for them to meet since so many events had to fall into place for this to happen: the servant accidentally giving Romeo and invitation to read, Romeo being heartbroken over Rosaline, Benvolio wanting to take Romeo to the dance to compare other girls to Rosaline ("And I shall make they swan a crow" Act 1, scene 2), Juliet's mother putting the idea of love in Juliet's head (albeit her intention was for Juliet to love Paris).  All of these things had to happen for them to meet, so therefore fate is clearly at hand here.

How could Fate be seen as playing a part in Romeo and Juliet's death?

I think that the Prologue is probably the best starting point in examining the role of fate in the two lovers' deaths.  Consider that Shakespeare himself opens with fate's hand being present in the drama:

From forth the fatal loins of these two foes(5)
A pair of star-cross'd lovers take their life;

This brings out the idea that the deaths were fated because Romeo and Juliet entered into a configuration that was outside of their own control.  The "ancient grudge" to which there is reference in the opening lines of the Prologue indicate that this set up was larger than the two lovers.  The very idea of fate is present in the fact that both young people really had no chance of controlling anything in their world other than their feelings.  They could not alter this set up, nor could they effectively abolish it.  They were pawns, for lack of a better word, within it.  If the argument about their deaths being fated is going to be advocated, I think you would have to look at the plans that both lovers make to being together as being trapped in futility.  There is an undercurrent that while both of them want to be together, something, some type of force, is going to inject itself into the discussion to prevent this from happening.  Perhaps, this feeling is developed from the Prologue's warning, but it settles into the characters themselves.  Before Juliet take the potion, she goes through all the various calculations and possibilities that exist, almost trying to rationalize the whole thing, but understanding that she is unable to do so.  The fact that she would contemplate all of these "mischances" helps to reveal that at her most critical moment, she feels the weight of fate upon her and tries to shake it off, recognizing that it is too powerful.  If this argument is going to be made, I would look at these areas as starting points for its substantiation.

How does Shakespeare explore fate in the final scene of Romeo and Juliet?

Shakespeare has already told the audience in the prologue that Romeo and Juliet are fated to die. As the final scene begins, they are both still alive, though Romeo believes that Juliet is dead, as does Paris, who has come to strew flowers over her body. Romeo kills Paris, then, realizing who he is, takes the dead man's hand and describes him as "One writ with me in sour misfortune's book." Romeo feels a sense of fraternity with Paris, as he thinks they are both the victims of fate, and that he, like Paris, is destined for death.

When Juliet awakes and sees the Friar, he tells her,

A greater power than we can contradict
Hath thwarted our intents.

Although in his speech to the Prince, Friar Laurence describes it as an accident that Romeo failed to receive his letter, his encapsulation of the story, piling one unfortunate event on another, tends to confirm the idea of this "greater power."

The Prince also accepts the idea of a greater power, which he calls "heaven," using the deaths of Romeo, Juliet, Patis, Mercutio and Tybalt to punish the feuding Montagues and Capulets, as well as punishing the Prince himself for failing to maintain order in Verona. Therefore, while the hand of fate seems senseless and purely tragic from the perspective of the young lovers, Shakespeare shows that it has at least brought peace and order to the city by the end of the play.