Hamlet IV

The point of no return had been reached. Ophelia's death and Polonius's death have made going back to an idyllic time when only King Hamlet was dead impossible. All of the important events in Hamlet occur solely due to the appearance of King Hamlet in ghost form, something no one was expecting, not even the cunning King Claudius. 

Would have life been better had Hamlet not began his quest for vengeance? For all then-living parties involved, there'd be peace, albeit an unjust one. However, that would mean that Polonius, Ophelia, and whomever else falls victim during the bloodshed at the end of play would be alive, most of them innocent of crimes that demand capital punishment. Claudius's crime would go unpunished but no one would suffer the imminent bloodbath. Would it be too selfish for the living to live a false peace while they're still alive?

Hamlet III

Laertes has returned to Denmark and now seeks vengeance for the death of his father, Polonius. King Claudius is particularly in support of Laertes, claiming the revenge would be just.

This justification would condemn King Claudius himself, due to his own murder of Hamlet's father. This irony is extremely apparent and serves to illustrate Claudius's hypocrisy and craftiness, bending the situation and rules as he sees fit. He has no qualms about manipulating other people and is quite well-versed in doing so. This does certainly fit his character of being a cunning man capable of murdering his own brother and to go to lengths to defend his ill-gotten power. However, he is not so cold and calculating as to remain in his calm state of mind when Hamlet put on the play intended to contrive some sort of guilt from King Claudius. In all respects otherwise, had not the supernatural intervened in the form of apparitions, King Claudius would've gotten away with it too (had it not been for some meddling 30-year olds).

Hamlet II

Prince Hamlet, whose father was killed, is exactly that. As a character, Hamlet has not yet shown any characteristics that define him nor anything to separate him from the mold of a mourning prince with a complicated love life and family issues. By 21st standards, the only standards I admittedly only know, Hamlet is, so far at least, rather two dimensional and does not have the feel of an actual person. He is introduced while still in the throes of grief of his father's untimely death. His next appearance is the inciting incident of the meeting with the ghost of his father, immediately following onto the path of finding his uncle's guilt and then confronting him. This path is rather narrow and by the end of Act II, very little character development is evident. The characters are all the same people from beginning to end.

Hamlet I

Hamlet, quite sensibly, does not immediately leap into action when the apparition of his father commands him to seek vengeance. This indecision would have been vital had Hamlet's uncle been innocent of any sort of treason or murder; however, this is the crux of the play. Within the dialogue of other characters, it is established that many of them believe Hamlet to be insane which would be a detriment to Hamlet's credibility should he seek to recruit for his cause to kill his uncle. He himself is unsure as to the actual guilt of his uncle and must spend part of the play determining it. 

But that's about as much plot as can be foreseen. A straightforward murder story ending in more murder with some love toils with Ophelia thrown in. Frankly, Hamlet's indecision and investigation are the sole reasons the play does not immediately erupt into a bloodbath (ignoring any comments into human psyche scholars have decided stem from Shakespeare's writing).