This quote is also discussed on our free Shakespeare Quotes section.
Romeo refers to himself as fortune's fool because his love and marriage to Juliet have filled his head so much that he does not pay full attention when he encounters Tybalt in the street. He is full of bliss for his great fortune and wants to stop the fight, but Tybalt is of no such mind.
When Mercutio is killed by Tybalt at a moment that takes Romeo by surprise he admits that his love for Juliet has made him soft.
Rom."This gentleman, the prince's near ally,
My very friend, hath got his mortal hurt
In my behalf; my reputation stain'd
With Tybalt's slander, Tybalt, that an hour
Hath been my kinsman. O sweet Juliet!
Thy beauty hath made me effeminate,
And in my temper soften'd valour's steel!" (Act III, Scene I)
Romeo makes this comment immediately after killing Tybalt, Juliet's cousin. Tybalt kills Mercutio after Mercutio defends Romeo's honor, and then it is Romeo's duty to fight Tybalt. After he has killed Tybalt, he realizes that he has killed all hope for reconciliation between the Montagues and the Capulets and thus, any chance that his marriage to Juliet will be accepted by their families. For Shakespeare, fortune means something along the lines of "fate" or "chance," so by saying he is "fortune's fool," Romeo is bewailing his incredibly bad luck.
because now juliet will hate him-- that's what he thinks!