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Hamlet: was the Prince sane or mad?

Whether Prince Hamlet is sane or insane (mad) at various moments in the play is highly debatable. Some argue that Hamlet's seeming madness is only good acting, following his expressed intention "To put an antic disposition on" after his first meeting with his father's ghost. This argument can be supported by his dialogues with Claudius, Polonius, Osric, Rosencrantz and Guildenstern, in all of which Hamlet's seemingly mad language, carefully studied, turns out to be skillful, scornful and sensible. Further, Hamlet uses a play to determine both Claudius' and Gertrude's guilt. He plans and organizes the event, and carries it out effectively, though he seems almost out of control at the crucial moment.

Others argue that Prince Hamlet goes over the edge into madness at times during the play. His treatment of Ophelia, a woman he had loved, is extremely cruel, and drives her to insanity and then death either through a mad accident or suicide. (Yes, she had followed her father's instructions to turn Hamlet away, and she had allowed herself to be used by her father and the king to learn Hamlet's state of mind, but there is no indication in the play that she intended to harm Hamlet.) Hamlet seriously considers suicide, though he rejects it. He uses gross sexual language and accusations against his mother, so that his father's ghost appears to intervene. Hamlet spots a movement in the curtains of his mother's room, and drives his sword through the cloth without determining who is behind it, killing Ophelia's father. (Yes, Polonius was spying, but Hamlet kills him hoping it is the king, without bothering to check.) During Ophelia's funeral, Hamlet leaps into her grave and wrestles with her brother. The Prince had good reason to kill one person, Claudius. When the play is finished, Hamlet has killed or is a contributing cause to the deaths of Ophelia, Polonius, Laertes, Rosencrantz, Guildenstern, Gertrude, Claudius, and himself.

In this answer, "mad" means having lost rational self-control. If a different definition is used, that will change the analysis. There is a famous book by a Freudian psychoanalyst concerning Hamlet's mental state -- Hamlet and Oedipus, by Ernest Jones. While this book today is not generally viewed as either good psychology or good literary criticism, you may find it interesting.

I think the play is most effective if one views Prince Hamlet as often "on the edge" between sanity and madness. This creates an exciting ambiguity as to his character and the play which would be lost if one chose either alternative.

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