The first instance of revenge that affects the characters in Shakespeare's Romeo and Juliet occurs long before the play begins.
CHORUS. Two households, both alike in dignity,
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean. (Prologue, 1–4)
The reason for the "ancient grudge" and the first act of revenge between the Capulets (Juliet's family) and the Montagues (Romeo's family) is never explained in the play, if anybody even remembers what the reason is.
Nevertheless, the feud seems to be in the forefront of everyone's mind. The first two characters who enter the play carry swords and bucklers (small, round shields up to 18 inches in diameter), and they're ready for a fight. Within a few minutes, there's a full-scale brawl in the streets between servants and family members of the Capulets and the Montagues.
The Prince appears on the scene to break up the brawl.
PRINCE. ...What, ho! you men, you beasts,
That quench the fire of your pernicious rage
With purple fountains issuing from your veins! (1.1.79–81)
The "pernicious rage" is a lust for revenge that seems to permeate the sensibility of every member, servant, and friend of each family.
Despite the Prince's warning against future brawls in the street under pain of death, it's not long before Mercutio and Tybalt are sword fighting in the street. Tybalt kills Mercutio when Romeo tries to come between them, and Romeo kills Tybalt in retaliation for Tybalt killing Mercutio.
The Prince is once again on the scene, and Benvolio explains what happened.
BENVOLIO. ...An envious thrust from Tybalt hit the life
Of stout Mercutio, and then Tybalt fled;
But by-and-by comes back to Romeo,
Who had but newly entertain'd revenge,
And to't they go like lightning; for, ere I
Could draw to part them, was stout Tybalt slain;
And, as he fell, did Romeo turn and fly. (3.1.173–179)
Lady Capulet calls for revenge against Romeo.
LADY CAPULET. I beg for justice, which thou, Prince, must give.
Romeo slew Tybalt; Romeo must not live. (3.1.185–186)
The Prince decides against ordering Romeo's death for his part in the sword fight and for killing Tybalt, but banishes Romeo from Verona.
Romeo spends his wedding night with Juliet before leaving Verona for Mantua. Lady Capulet comes to Juliet after Romeo hurriedly exits through a window in Juliet's room. Lady Capulet is not satisfied that the Prince has exiled Romeo from Verona and vows revenge for Tybalt's death.
LADY CAPULET. We will have vengeance for it, fear thou not.
Then weep no more. I'll send to one in Mantua,
Where that same banish'd runagate doth live,
Shall give him such an unaccustom'd dram
That he shall soon keep Tybalt company;
And then I hope thou wilt be satisfied. (3.5.90–95)
Paris also gets caught up in the feud and confronts Romeo at Juliet's tomb. Paris believes that Romeo has come to desecrate the tomb, and Paris also seeks his own revenge against Romeo for what he thinks is Romeo's part in Juliet's death, which prevented Juliet from marrying Paris.
PARIS. This is that banish'd haughty Montague
That murdered my love's cousin—with which grief
It is supposed the fair creature died—
And here is come to do some villanous shame
To the dead bodies. I will apprehend him.
Stop thy unhallowed toil, vile Montague!
Can vengeance be pursu'd further than death?
Condemned villain, I do apprehend thee.
Obey, and go with me; for thou must die. (5.3.49–57)
The deaths of Romeo and Juliet finally bring an end to the cycle of revenge.