By definition, tragic heroes are those characters who experience a reversal of fortunes -- typically as a result of their hamartia, or tragic flaw. Conventionally speaking, a tragic hero suffers a horrible outcome directly as a result of a poor decision or a foolhardy action.
In the case of Shakespeare's "Hamlet," however, the eponymous Prince of Denmark finds himself beseiged from all sides from characters who force him to act. Whereas most tragic heroes are victims of their own undoing, Hamlet actually spends the better part of the five-act play (Shakespeare's longest) not doing, which is to say doing little more than pontificating, plotting, and exchanging in alternately high-minded sophistry and low-brow toilet humor in a vain attempt to distinguish truth from faleshood. Unlike the average tragic hero, Hamlet actually does very little of his own accord over the first three acts of the play, choosing instead merely to react to those situations which unfold around him, all the while growing increasingly paranoid and allienated from his innermost circle of friends and family members.
Stated simply: Hamlet does not know who he can trust, and he is crippled by his inability to act. If he has a tragic flaw, it is that he is obsessed with discerning absolute truth before commiting even the slightest of actions (as he famously tells Rosencrantz and Guildenstern "'Tis nothing either good nor bad, but thinking makes it so"). Tragically, the one time that Hamlet opts *not* to painfully discern veracity from falsehood results in him inadvertantly slaying Polonious through the tapestry, and thus he ultimately sets in motion the tragic series of events that will result in all of the major characters in this play.