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.
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.