What are examples of dreams and premonitions in Romeo and Juliet?

Dreams and premonitions tend to pervade Shakespeare's Romeo and Juliet, as they do many of the Bard's plays. There are several good examples which, in some cases, act as foreshadowing for later events in the play. The most famous of these dreams is within Mercutio's speech about Queen Mab, where he claims she is the fairies' mid-wife who brings dreams to lovers, soldiers, and others. Mercutio's fantastical speech is at first a comic critique of Romeo's lovelorn attitude and his infatuation with Rosaline, but later takes a more sinister and fatal tone, not unlike the play itself, which is initially the story of innocent young love but then becomes dark and full of death. Immediately following Mercutio's rant is Romeo's premonition that attendance at Capulet's party is the beginning of something which will ultimately end in his death:

I fear too early, for 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 despisèd life closed in my breast
By some vile forfeit of untimely death.

Later, in Act III, Scene 5, just as Romeo is leaving for Mantua, Juliet seems to have a premonition that she sees Romeo "As one dead in the bottom of a tomb." This statement foreshadows the final scene in which Romeo is indeed dead in Capulet's tomb. Juliet also has premonitions of what she will encounter in the tomb if she takes the Friar's potion. In Act IV, Scene 3 she predicts "loathsome smells," "shrieks like mandrakes," and "hideous fears." Nevertheless, she is willing to fake her death in order to be with Romeo.

Finally, Romeo opens Act V by detailing a dream where Juliet found him dead and "breathed such life with kisses in my lips/ That I revived and was an emperor." This dream seems to foreshadow later events in the tomb when Juliet wakes up only to find Romeo dead. She briefly attempts to kiss the poison from his lips before killing herself with his dagger. In the end, dreams and premonitions play a major role in the play and seem to be more important than simply "children of an idle brain/ Begot by nothing but vain fantasy;/ Which is as thin of substance as the air" as Mercutio puts it just after his Queen Mab speech.