Hamlet was driven to, if not madness, something quite resembling it upon learning that his uncle murdered his father, then took his throne and married his mother.
At the beginning of the play, Hamlet was understandably upset with the recent death of his father, and was only more hurt to discover suspicion that it was his uncle who caused his father's death. It is also reasonable that Hamlet would feel poorly about his mother's marriage to his uncle so soon after her husband died. However, Hamlet takes these emotions to quite an extreme, and does many things that cannot be considered sane even despite his circumstances.
He decides to pretend to be mad in hopes that this will enable him to spy on the conversations of others and uncover the truth surrounding his father's potential murder. Although, we never see this have the desired effect, let alone any positive effect, in the play. Moreover, it is difficult to believe that a sane person came up with that plan to achieve his goals because it seems so ineffectual. He also, as narry a sane man would, scorns and casts aside his love, Ophelia, scaring her and severing any hopes of further connection with her. It is doubtful that a person in their right mind would push away his love instead of perhaps turning to her for comfort.
From the words of other characters, we can gather that Hamlet was a sane and great man before the events of the play turn him less so and drive him to do rather mad things.
