Hamlet is often faulted for what many scholars and writers believe is his tragic flaw of indecisiveness. This flaw is demonstrated in his inability to avenge his father's murder by killing his uncle, Claudius, who usurped his father's throne and married Hamlet's mother—a marriage which Hamlet condemns as "incestuous" (1.2.160; 3.3.92).
Hamlet has ample opportunity to kill Claudius throughout the play—most notably while Claudius is alone and on his knees praying in act 3, scene 3—but, for one reason or another, Hamlet simply fails to act.
At first, Hamlet is reluctant to believe his father's ghost without more proof.
HAMLET. The spirit that I have seenMay be a devil; and the devil hath powerT' assume a pleasing shape; yea, and perhapsOut of my weakness and my melancholy,As he is very potent with such spirits,Abuses me to damn me. I'll have groundsMore relative than this (2.2.593–599).
When Claudius reveals his guilt while watching the performance of The Murder of Gonzago, which Hamlet arranged specifically for that purpose, Hamlet again vows to avenge his father's murder, but he does nothing.
Later, Hamlet is reluctant to kill Claudius while he's praying and risk sending him to heaven rather than to hell (3.3.76-98), and once again does nothing.
This argument for Hamlet's tragic flaw of indecisiveness assumes, however, that Hamlet must necessarily avenge his father's murder, and, by doing so, become a murderer himself.
Shakespeare's audience knew that under Elizabethan law a revenge murder was nonetheless considered murder. According to religious precepts of the time, revenge was considered a sin, whether it involved murder or not (Romans 12:19). Vengeance belonged to God, not to man (Deuteronomy 32:35).
Nevertheless, Elizabethans considered revenge a sacred, moral duty.
This paradox is highlighted in the play by Hamlet's indecisiveness, which Shakespeare emphasizes by comparing Hamlet's indecision and inaction with Laertes's straightforward approach to the matter.
While he's away in France, Laertes learns that his father, Polonius, has been killed. In act 4, scene 5, Laertes returns to Elsinore to avenge his father's death. He breaks into the castle and confronts Claudius. Laertes doesn't care who killed Polonius, even if Claudius himself did it. Laertes is intent solely on revenge, and he's unconcerned about any consequences that might befall him.
LAERTES. Let come what comes; only I'll be revengedMost throughly for my father (4.5.145–146).
Claudius tells Laertes that Hamlet killed Polonius. The question arises as to why Laertes doesn't simply track down Hamlet in the heat of that moment and kill him, but that would bring the play to a screeching halt and to an unsatisfactory dramatic resolution. Instead, Laertes conspires with Claudius to kill Hamlet, and the conspiracy plays out in the final scene of the play.
Early in the play, Shakespeare arouses the audience's emotions toward Hamlet, and at the same time, involves the audience in Hamlet's revenge against Claudius. At first, the audience wants Hamlet to avenge his father's death. Over the course of the play, however, the audience becomes far more interested in Hamlet himself than in any other aspect of the play.
Hamlet is an Elizabethan revenge play in which the acts of revenge are wholly incidental to the play itself. Claudius's death at the end of the play—particularly in the midst of the deaths of Gertrude, Laertes, and Hamlet—is almost an afterthought. Hamlet wasn't motivated to kill Claudius at that moment to avenge his father's death, but by the immediate circumstances of that scene.
No doubt Hamlet's indecisiveness and inaction contribute to his downfall, but his downfall isn't entirely self-inflicted. Characters like Claudius and Laertes, who conspire against him, as well as events over which Hamlet has no control, bring about his fateful and fatal end.