It is worth remembering when answering the question concerning Hamlet’s madness Eliot’s fuller thoughts on the matter. It is not that he considered Hamlet insane; rather, Eliot thought that Shakespeare failed to provide the “objective correlative” that  would express Hamlet’s feelings for his mother.  By “objective correlative” Eliot refers to “a set of objects, a situation, a chain of events which shall be the formula of that particular emotion.”  An example would be Lady Macbeth’s sleepwalking, which is an objective correlative for her state of mind. Hamlet, according to Eliot, lacks such an experience—a sort of metaphor for his state of mind.. Because Shakespeare cannot understand Hamlet’s feelings, he cannot create an objective correlative for them, and so Hamlet therefore appears mad to the audience while his madness does not intrinsically develop out of the plot.  According to Eliot, “We must simply admit that here Shakespeare tackled a problem which proved too much for him.”  Hamlet’s apparent madness results from Shakespeare not finding the dramatic means to express Hamlet’s emotions.

I agree with the statement and think it's very well put. It would be strange if Hamlet didn't feel a sort of madness, who wouldn't given the circumstances he faces? However, it's not utter and complete madness, Hamlet still has power over his own actions, which is not true of real madness. 

Enotes has a great deal of information regarding the debate about Hamlet's feelings toward his mother and how those feelings relate to his madness. If you go to the link below, you'll get a much broader perspective on Hamlet's mysterious character. Regardless of the reasons for Hamlet's madness, I agree with Eliot's statement that Hamlet isn't certifiably insane, but he does have severe issues that warrant a few sessions on a psychiatrist's sofa.

I base this partly on the dilemma Hamlet's faced with, and then putting myself in his "shoes". Stop and consider your reactions to the following:(1)your beloved, respected father dies;(2)your mother quickly marries your uncle;(3)the ghost of your dead father tells you to avenge his murder by his brother. Wouldn't this put most of us on the couch? After speaking with the ghost, Hamlet is then supposed to go kill his uncle, the king, his mother's husband, because a ghost told him to! Wouldn't this situation drive any person to some degree of madness?

Hamlet's character is complex as well. He seems obsessed with death and suicide even before he sees the ghost. Once he sees the ghost, his grief over his father's death and his mother's marriage is intensified, and he's never given the chance to go through the grieving process. His problems only get worse as the play goes on, and we see his extensive pain and suffering. This is the main reason I think he's not totally insane, just a little mad.