Hamlet

One reason may be that that opportunity has not yet arisen for him to kill Claudius before the scene in Act III scene 3 when Claudius seems to be praying. At that point, Hamlet doesn't want to kill Claudius because he believes doing so will send him to heaven, since he appears to have been praying, and Hamlet feels that heaven is not a worthy punishment for his father's murder.
Another reason may be that Hamlet simply thinks too much about it. He hesitates because he looks at the task from too many angles. He is paralyzed by his own uncertainty. He is uncertain if killing Claudius is really the right thing to do. He is uncertain, as is evidenced in his solioquy at the end of Act II scene 2, that the ghost is really his father.
The passage below taken from Hamlet's solioquy at the end of Act II sheds more light on the reasons for his hesitation:
"I have heard
That guilty creatures, sitting at a play,
Have by the very cunning of the scene
Been struck so to the soul that presently
They have proclaim'd their malefactions;
For murder, though it have no tongue, will speak
With most miraculous organ, I'll have these players
Play something like the murder of my father
Before mine uncle: I'll observe his looks;
I'll tent him to the quick: if he but blench,
I know my course. *The spirit that I have seen
May be the devil: and the devil hath power
To assume a pleasing shape; yea, and perhaps
Out of my weakness and my melancholy,--
As he is very potent with such spirits,--
Abuses me to damn me:* I'll have grounds
More relative than this.--the play's the thing
Wherein I'll catch the conscience of the king."
The quotation above from the soliloquy at the end of Act II scene 2 voices some of Hamlet's doubt and reasons to hesitate. The ghost may be a devil tricking him into a murder that will damn him. He plans The Mousetrap, the play within the play, to test both the King and the ghost. Of course, the ghost's claim turns out to be true, and this reassurance solidifies Hamlet's...