There are many quotes and points of action in the play that reveal the hatred between the Capulets and Montagues and cries for and actions of revenge. So, I will focus on a main character whose sole function could be said to be to display the hatred of the Capulets for the Montagues -- Tybalt.
In Act I, Scene i, Tybalt happens upon the servants of both houses brawling in the streets, and rather than "keep the peace" as ordered by The Prince, he pours oil on the fire by taunting Benvolio:
What drawn and talk of peace? I hate the word,
As I hate hell, all Montagues, and thee.
Later in the Act at the Capulet party, he recognizes Romeo and tells Lord Capulet that he will call Romeo out then and there. Capulet wants to keep the party atmosphere and has his patience so tried by Tybalt's insistence upon throwing Romeo out that he loses his temper and commands Tybalt to ignore Romeo. Tybalt exits the scene with a nice foreshadowing of the duel to come with Romeo:
I will withdraw. But this intrusion shall
Now seeming sweet, convert to bitt'rest gall.
And finally, he is so bent on revenge against Romeo for besmirching his family's gathering, that he takes up Mercutio's challenge when Romeo refuses to fight. Once Tybalt slays Mercutio, he's still ready for Romeo, inflaming Romeo's anger by calling him "boy." They fight, and Romeo kills Tybalt and must flee.
In Romeo and Juliet, Tybalt is the closest thing to a villain in the play. This is important because, in order for Romeo to remain the hero the audience is rooting for, Tybalt should be seen as an instigator of the "evil" actions of the play. He should appear to the audience as someone who bears the responsibility for the duel that goes against the ruling for peace and causes Romeo's banishment.