What (if anything) is Hamlet's fatal flaw?
Concerning Shakespeare's Hamlet, I'll put my vote in for Hamlet's tragic flaw being hubris. Hamlet has an opportunity to get his revenge and kill Claudius, but hubris keeps him from doing so.
Claudius's reaction to the murder scene in the play-within-the-play convinces Hamlet that the Ghost is telling the truth and that Claudius is, indeed, guilty of killing King Hamlet. Once he's sure of Claudius's guilt, Hamlet seems ready to kill the king. He has a perfect opportunity to do so while Claudius is praying, but decides not to because he doesn't want to send Claudius straight to heaven. Hamlet thinks Claudius is confessing his sins, and killing him when his slate or soul or whatever is clean, Hamlet believes, would send Claudius to heaven. Hamlet won't do that.
When Hamlet makes the decision not to kill Claudius for the reason he gives, he is stepping beyond his station in life: he is guilty of hubris. Human salvation is not Hamlet's business--it's God's business. If Hamlet kills Claudius in Act 3, numerous innocent lives are saved, including his own. His hubris leads to the blood bath at the conclusion of the play.
Ironically, Claudius is not confessing his sins. He is unwilling to give up the spoils of his sin, and won't repent. Thus, Hamlet could have killed Claudius in Act 3, gained his revenge, and not sent Claudius to heaven. Unfortunately, he gives up the chance to do so. This, I believe, is the climax of the play and reveals Hamlet's tragic flaw.
I would say that a fatal flaw in the character of Hamlet is in inability to act. When he does act, it has been the result of so much pent up inaction that its results are disastrous. There seems to be little in way of healthy balance in Hamlet as a person. When reading Macbeth, the reader is made aware of the difficult of letting function smother surmise, as there is little in way of reflection and rumination when Macbeth descends into his moral abyss. In Hamlet, the reader sees the flip side to this when surmise smothers function in that he is unable to overcome the philosophical conundrums within which he finds himself. Hamlet's words are what he uses to fully understand and gauge situations, yet in a uniquely modern context, it is these very words that imprison his ability to act. Hamlet is more inclined to intellectually and cerebrally give argument after argument until an infinitely regressive cycle comes about where no action is taken. This paralysis of action almost becomes second nature to him as evidenced with his relationship with Ophelia, a situation craving for someone to act, but no one doing so.
Another possibility to consider as Hamlet's fatal flaw is his decision to avenge his father's "foul and most unnatural murder." It is a course of action that he himself has trouble stomaching, that alienates him from all around him, that results in the death of Polonius and the insanity of Ophelia.
His mission to seek revenge places him in a situation in which he cannot win. Even had he killed Claudius early in the play, Hamlet would have met a less than desirable end. Without being able to produce any true evidence of Claudius' guilt, he would have been executed.
In seeking revenge, Hamlet is in a no-win situation. He cannot let the murder of his father go without exacting some revenge and yet he has such a keen sensibility that such an act will definitely harden him. In order to do such a deed, he literally must transform himself into a madman.