Shakespeare's Romeo and Juliet doesn't begin with foreshadowing, but with foretelling.

CHORUS. ...From forth the fatal loins of these two foes
A pair of star-cross'd lovers take their life;
Whose misadventur'd piteous overthrows
Doth, with their death, bury their parents’ strife. (Prologue, 5-8)

The Chorus tells the audience what's ultimately going to happen. There's no mystery about that. What the audience doesn't know is how it's going to happen, or if anything else unrelated to the "star-cross'd" lovers' deaths might happen along the way.

However, Shakespeare does manages to infuse a little bit of foreshadowing into the Chorus's foretelling of the end of the play.

CHORUS. A pair of star-cross'd lovers take their life... (Prologue 5)

This is a very subtle play on words, the meaning of which becomes clear only when Romeo and Juliet take their own lives—if anybody actually remembers what the Chorus said in the fifth line of the play while they're watching Romeo and Juliet kill themselves "two hours" later.

With this Prologue, Shakespeare sets up quite a challenge for himself. Since he tells the audience what happens at the end of the story, Shakespeare has to write a really good play to keep the audience's interest, particularly since the basic story of Romeo and Juliet was well-known to his audience.

There had been three fairly recent publications of the story of Romeo and Juliet, including Arthur Brooke’s narrative poem, The Tragicall Historye of Romeus and Juliet, published in 1562—which scholars consider the primary source of Shakespeare's play—as well as Giuletta e Romeo, by Matteo Bandello, published in 1554, and Luigi da Porto’s Giulietta e Romeo, published in 1530. Other theatre companies in London were also performing their own versions of the Romeo and Juliet story.

Nevertheless, the question arises that if the audience knows what's ultimately going to happen, is the foreshadowing in the play really foreshadowing, or is it simply a reminder of what the audience has already been told?

Most of the faux-foreshadowing in the play involves the deaths of Romeo and Juliet, but even what seems like foreshadowing of events affecting other characters really isn't.

In act 3, scene 1, Benvolio cautions Mercutio that that they should get out of the streets to avoid meeting any Capulets:

BENVOLIO. I pray thee, good Mercutio, let's retire.
The day is hot, the Capulets abroad.
And if we meet, we shall not scape a brawl... (3.1.1-3)

There is a brawl, of course—which comes as no real surprise to anybody—in which Mercutio is killed by Tybalt, and Tybalt is killed by Romeo,

Tybalt seems to have foreshadowed this unfortunate turn of events at the Capulet's feast in act 1, scene 5, when Lord Capulet tells Tybalt simply to endure Romeo's presence, and not cause any trouble.

TYBALT. Patience perforce with wilful choler meeting
Makes my flesh tremble in their different greeting.
I will withdraw; but this intrusion shall,
Now seeming sweet, convert to bitt'rest gall. (1.5.94-97)

The confrontation between and among Tybalt, Mercutio, and Romeo was inevitable, and Tybalt simply foretold that something bad was going to happen, which it did. The audience might not have foreseen the extent to which something bad was going to happen, but they certainly knew that something bad would happen.

The situation is much the same as in Hamlet, after Hamlet tells Horatio what the ghost of his father said to him.

HAMLET. There's ne'er a villain dwelling in all Denmark
But he's an arrant knave.

HORATIO. There needs no ghost, my lord, come from the grave
To tell us this. (1.5.134-138)

Foreshadowing isn't foreshadowing if the audience knows what's going to happen, or if what happens—like a serious confrontation in the street between sword-carrying major characters from warring families—can easily be foreseen.

Shakespeare's use of foreshadowing in his play Romeo and Juliet could best be described as generous. It's never a surprise that the couple dies; it's even stated plainly as a fact in the prologue. The suspense in the narrative instead lies in how the tragedy comes to pass.

Other examples of foreshadowing in the play are too numerous to list here, but they include Juliet's claim that her "grave is like to be [her] wedding bed." In this quote, she is trying to say that she's worried she won't get to marry Romeo because he might already be married, but her words are also heavy with foreshadowing. Another, creepier example is when the lovers tell each other that they look pale. They think they're pale because of their sadness, but to the reader, this signals something much more tragic.

From the Prologue, the fate of Romeo and Juliet becomes known. They are destined for doom, and Mercutio provides a reminder of this through some foreshadowing he delivers in his dying lines:

A plague o’ both your houses!
They have made worms’ meat of me. I have it,
And soundly too. Your houses! (III.i.107-109)

Mercutio calls for a "plague" to befall both the Montagues and the Capulets because their feud has led to his death. This curse foreshadows the eventual death of the young lovers, effectively fulfilling Mercutio's curse.

In Act 3, Scene 5, Romeo is reluctantly preparing to leave Juliet's room when he tells her,

Come, death, and welcome! Juliet wills it so.—(III.v.24)

This line foreshadows the welcome invitation that Romeo will extend to his own death when he believes that Juliet has "willed" herself to die. Unfortunately, he misses the vital memo that she is only faking her death as he makes his own decision to die.

Foreshadowing abounds in this tragedy, which is one reason the audience is kept in high anticipation of the known eventual outcome, hoping against all evidence to the contrary that the story of the lovers will turn out differently than the foreshadowing predicts.

In Act 1, scene 4, Romeo's friends attempt to convince him to attend the Capulets' party with them.  He doesn't particularly want to go because he is feeling quite depressed as a result of his unrequited love for Rosaline.  By the end of the scene, however, they've convinced him to go and try to have some fun.  However, 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. 
But he that hath the steerage of my course
Direct my sail.  (1.4.113-120)

In other words, Romeo has a feeling that going to this party will be the beginning of a fateful chain of events that will end with his death.  However, whoever (or whatever) is in charge of his life's path is directing him to the party nonetheless.  Romeo's words foreshadow his eventual tragic death and the fact that the path to it does, indeed, begin tonight, when he meets Juliet Capulet.

Another example of foreshadowing comes when Romeo and Juliet are saying goodbye to one another after their one night together as a married couple.  Juliet says,

O God, I have an ill-divining soul!
Methinks I see thee, now thou are so low,
As one dead in the bottom of a tomb.  (3.5.54-56)

As Romeo climbs down from her window, Juliet feels as though her soul is predicting something terrible: with him below her, she feels as though he seems like a dead person at the bottom of his grave.  This foreshadows the fact that Juliet will never again see Romeo alive.  The next (and last) time she will see him is just after he has poisoned himself in her tomb, believing that she is dead.