In Act II, Scene 2, one reason that Romeo is afraid the exchange of affection he has just experienced with Juliet is a dream is that, for Romeo, this is the first time his love for a woman has been reciprocated. Romeo has just experienced a great deal of heartache as a result of his feelings for Rosaline. As Friar Laurence later points out, many times had Romeo come crying to him about Rosaline unreturning his love,
"Lo, here upon thy cheek the stain doth sit of an old tear that is not wash'd off yet" (Act II, Scene 3).
Romeo, himself, even described his love for Rosaline as torture. Therefore, to finally find someone he thinks is even better than Rosaline, and not only that, to learn that she loves him too, will certainly feel like a dream.
Another reason his exchange with Juliet may feel like a dream is that their exchange of vows was very sudden. Even Juliet, herself, says that their exchange of promises is
"too rash, too unadvised, too sudden; too like the lightning, which doth cease to be."
Hence, like Juliet, another reason he feels their exchange of promises to marry was a dream is that he agrees that it all happened far too suddenly.