Hamlet is Shakespeare's most critically acclaimed play, in that the play has psychologically confounded its readers for centuries. Most famously, Coleridge said it was a meditation on death; Freud said that Hamlet suffered from an Oedipus Complex; and T. S. Eliot said that it was an artistic failure. In particular, Eliot says there is no objective correlative (no justifiable evidence of Hamlet's indecision). He says that Shakespeare only has Hamlet tell us he is indecisive, rather than dramatically showing us signs of indecision.
I tend to agree with Eliot. I don't know if I would call the play a failure, but I think it is overrated, and I do not find the character of Hamlet to be as engaging as Macbeth, King Lear, Othello, or even Iago, Falstaff, or Viola. I find him excessively mopey, certainly not heroic, especially in light of what he does to Ophelia. My favorite role in the play is the Ghost; after that, I think, the play loses its intensity.
Although I love revenge drama, Hamlet works outside the rules of revenge. Instead of haunting Claudius, as he should, the Ghost haunts Hamlet. It's revenge by proxy, not dramatically satisfying. In other works, the ghosts haunt those who killed them: Caesar haunts his murderers; Banquo haunts Macbeth. Revenge is done physically and spiritually. In Hamlet, it is neither.
Also, the play is overly long. Tragedy is all about economy; it must be streamlined to elicit pity and fear. Oedipus is this way. Macbeth is half as long as Hamlet. Othello uses half the cast as Hamlet. Yes, Hamlet's language is beautiful, but there are so many monologues, soliloquies, plots and subplots that much of the action comes at the expense of the words, words, words.
I agree that Shakespeare's Hamlet is the greatest play ever written in the English language. I can't speak about plays written in other parts of the world in other languages. I also can't really define "greatest." In fact, "greatest" is a word I would usually avoid. It's one of those superlatives that is so vague writers should use it sparingly. I'm not sure how one would really measure to determine if Hamlet is or is not the greatest play ever written.
That said, the title character of Shakespeare's play is the most well-developed, most complex character in literature that I know of. I love it when he expounds on the meaning of "seems," when he jokes about worms eating Polonius, when he holds Yorick's skull in his hand. I feel sympathy when I recognize his depression. And I can't believe what a great idea Shakespeare had when he shows Hamlet not killing Polonius because he doesn't want to send him to heaven instead of hell.
I don't know exactly what the "greatest" is, and I'm probably not qualified to make that judgment, anyway (Macbeth, for instance, is a more perfect example of classical tragedy--there's a fine line between great plays), but it is my favorite.