Certainly the graveyard scene has its share of unanswered questions. Hamlet is contemplating the skull of the court jester, Yorick (Act 5, Scene 1):
Alas, poor Yorick! I knew him, Horatio: a fellow of infinite jest, of most excellent fancy. He hath borne me on his back a thousand times. And now how abhorred in my imagination it is! My gorge rises at it. Here hung those lips that I have kissed I know not how oft. Where be your gibes now? your gambols? your songs? your flashes of merriment, that were wont to set the table on a roar? Not one now to mock your own grinning? Quite chop-fallen?
In this last act, the act in which Hamlet's fate is sealed, he is thinking of death and facing it squarely as he questions the moldy, dirty, smelly skull. What does it all amount to, really, this thing we call life? What's the point? In the end, we are but things that are of the earth and return to the earth. We fancy ourselves to be something else for a while, but we will be mere objects for a much longer time.
In contrast, there's the famous "to be or not to be" soliloquy in Act III, scene 1, in which Hamlet's rhetorical questions also concern mortality. Here, though, he's talking about suicide as a much more pleasant and logical option than suffering through the quagmire of life, calling the pleasant sleep of death "a consummation /Devoutly to be wished." He questions why people are willing to "bear the whips and scorns of time, /Th' oppressor's wrong, the proud man's contumely...When he himself might his quietus make /With a bare bodkin?" In the scene at the end with Yorick's skull, Hamlet seems resigned to his fate, whatever it may be, but in Act III, scene 1, the talk of suicide denotes that Hamlet thinks he still has control over when his life will end (unanswerable question).
Hamlet continues and answers his own question about why people suffer through life despite an easy way out: fear of the unknown...what happens when we die? This has to be THE ULTIMATE unanswered question of all time and directly factors into Hamlet's fatal decision later NOT to kill his uncle while he is praying for fear he'd be sending a murderer to Heaven. As the rightful heir to the throne of Denmark, Hamlet is responsible to see justice done, no matter the cost.