He kills his father as he flees his home and marries his mother after solving the riddle of the Sphinx. His end is inevitable, but Sophocles clearly shows the role negative character traits play in Oedipus' tragedy, while Hamlet's supposedly negative traits of doubt are not necessarily evil. Thus Hamlet could be classified as a kind of nascent anti-hero, a man who mourns "the time is out of joint/oh cursed spite/that ever I was born to put it right," and never succeeds in 'putting it right' because society offers him only one, ineffective mechanism for pursuing a brutal type of justice (1.5). The failure of heroism to 'put things right' is manifested starkly in Waiting for Godot, where the heroes famously wait for the final 'solution' of the arrival of the presumably heroic Godot, who never comes. These characters are not so much heroes or even anti-heroes -- rather they displace their desire for heroic qualities upon a fictional person. They still believe in the ability of a savior-hero to deliver the world, but since they know they do not have such characteristics they 'create' Godot. Similarly, another Beckett protagonist, Krapp, displaces desirable heroic qualities within himself onto an external object, since he cannot conceive of himself as a hero. In Krapp's case, the object is a tape recorder. The heroic individual becomes the Krapp of the past, the speaker on the tape. Krapp mocks his old self, but also clearly regrets the qualities present in himself that he has alienated and relegated to the past.

It is often said that we 'moderns' do not believe in heroes like the ancients. Yet even in Oedipus the King, Oedipus is first...

Hamlet resists his role as an avenger, even while he despises Claudius. He expresses contempt at the more traditionally heroic characters of the play, like the overly emotional Laertes. He is introspective enough to admit Laertes has the same cause as himself -- ironically, the same filial obligation to kill Hamlet that Hamlet has to kill Claudius (5.1). Hamlet's irony and self-searching nature regarding the moral worth of his quest of revenge is deeply anti-heroic as Beckett's parodies of the impulse to find a hero in nothingness.
Thus the question arises: have we ever had true heroes at all, except in comic books? Even Oedipus is an ambiguous figure in terms of his power and perceived heroic potential. Heroes today are even more quickly torn down than the heroes of the past, give the speed of communication. Contemporary cynicism has lead to few real heroes in modern culture, other than ones that are set in fantasy never-never lands like Star Wars and Lord of the Rings. The far-off settings allow storytellers to ironize the nature of heroism, by placing the tale in 'quotes' and making it explicitly irrelevant to reality. This is the future of heroism -- a heroism even more doubtful than existed in previous eras, a heroism that is not meant to teach, merely to entertain. At least Sophocles, Shakespeare, and Beckett examine the concept of heroism as a serious construct -- today, authors do not even have the moral conviction to seriously present a 'hero' to audiences.