I believe Romeo's tragic flaw is his quickness to fall in love, and then to let the chips fall where they may because of it. At the beginning of the play, he's madly in love with Rosalind, who we never even see. Then he goes to a party and falls head over heels in love with Juliet...damn the torpedos and full speed ahead! He leaps before he looks and doesn't consider all of the possible ramifications of his actions.
All tragic heroes have tragic flaws of some kind, and Shakespeare's protagonists are chock full of flaws. Macbeth's tragic flaws are his ambition and his willingness to let himself be manipulated by those around him. King Lear's tragic flaw is his pride. Othello, too, allows himself to be manipulated by Iago, rather than trusting his wife.
The link below will take you to eNotes' main Shakespeare page, which will lead you to a great deal of information about all of Shakespeare's plays and characters. Good luck!
I believe Romeo's tragic flaw was his rushing, ignoring of better judgment, and his challenging towards the fates. He constantly rushed his and Juliet's relationship, and as we all may know, they both died at the end because of their hasted planning. This is so, because the friar's plan was rushed by romeo and juliet, and so he didn't take into account the possible errors the plan had, such as the failure in delivering the mail. Also, his ignoring of better judgment leads to his downfall. An example is when before the party he talks about having a bad dream and not wanting to go, but Mercutio insists with the famous Queen Mab speech, and so Romeo gives into peer pressure. As a result, he meets Juliet and the whole problem starts. Finally, Romeo (before act 3, scene 1, which is the big fight between Tybalt and Mercutio), challenges the fates, and the deaths occur as a result.
As for other Shakespeare characters, look at the tragedies, because all the main characters of the tragedies have many fatal flaws.