Two aspects of William Shakespeare's "Hamlet" that have puzzled critics for several centuries are Hamlet's indecisiveness as a character and his delay in seeking revenge. One answer is that Hamlet wants to be absolutely sure of his facts before he takes revenge. Claudius is not only King of Denmark but Hamlet's uncle, and killing him without absolute certainty and moral justification would be ethically wrong.
One of the main reasons for the delay is the very nature of the evidence Hamlet has urging him on to revenge, namely his encounter with the ghost of his father. Ghosts are not inherently trustworthy; many Christians in Hamlet's period would have considered ghosts emissaries of the devil. This suspicion of the ghost appears in Horatio's speech arguing that Hamlet should not follow it:
What if it tempt you toward the flood, my lord,
Or to the dreadful summit of the cliff ...
And there assume some other horrible form,
Which might deprive your sovereignty of reason
And draw you into madness?...
Before Hamlet makes the final decision to murder his uncle, he must have firm evidence of his uncle's guilt, beyond the word of the ghost. Thus at the end of Act II Scene 2, Hamlet devises a plot to use a play to get Claudius to reveal his own guilt, stating:
... I'll have these players
Play something like the murder of my father
Before mine uncle: I'll observe his looks;
... if he but blench, I know my course.
... the play 's the thing
Wherein I'll catch the conscience of the king.
There are a number of reasons where Hamlet confesses his delay. His soliloquy at the end of 2.2, his 2B soliloquy in 3.1, his soliloquy in 3.3 while Claudius is praying and then in his final soliloquy at the end of 4.4. Also read the Player King's speech, "I do believe you think what now you speak..." But that is just a surface analysis of the delay theme. What Shakespeare explores is the human propensity to reevaluate our decisions. One must be careful in accusing Hamlet of indecision. He is not indecisive. He proclaims to the Ghost, "Haste me to know't, that I...May sweep to my revenge." There is a much finer point here. The delay occurs after the decision is made. It's the chasm between resolution and action. Look at Claudius and his decision to send Hamlet to England at the end of 3.1 (Hamlet doesn't leave until the end of 4.4 why?) or compare Laertes' revenge on Hamlet when he actually gets his fingers on Hamlet's throat in Ophelia's grave. Laertes had bragged that he would cut Hamlet's throat in the churchyard. There are millions of reasons for not acting on our decisions. But, as Hamlet confesses in his last solioquy, greatness comes from action not excuses. So, put yourself in Hamlet's place and think through actually killing the king.