First, before the brawl in the street, Sampson is showing off and bragging that he is a great fighter. He tells Gregory that he is so great that he would even kill maidens, which seems too great a hyperbole for his reputation. Sampson says, "'Tis all one, I will show myself a tyrant. When Ihave fought with the men, I will be cruel with the maids; I will cut off their heads" (I.i.17-18).
Then, Mercutio's Queen Mab analogy can be considered a hyperbole, to because he exaggerates dreams to prove his point that they are not real. His analogy goes a little more exaggerated at the part that he talks of soldiers dreaming of cutting others' throats, too. "Sometime she driveth o'er a soldier's neck,/ And then dreams he of cutting foreign throats" (I.iv.86-87).
Finally, Romeo cires out a hyperbole when he says, "A thousand times the worse, to want they light" (II.ii.164). He is referring to how horrible it will be to be without Juliet. The number "thousand" is the hyperbole here. It is a bit like saying "There were a billion people at the concert last night" just to get a strong feeling/point across.