Clearly Hamlet is not. He admits to putting on a "antic disposition" so it'll throw off Claudius. It gives him time to plan, and as we watch throughout the play, sort out his feelings. Taking a stand against Claudius at the outset would have gotten him killed instantly.
I don't actually think so. There are of course parts of the text that critics who believe Hamlet is mad point towards, such as his behaviour in Ophelia's chamber. However, we need to remember that he reveals to Horatio and Marcellus that he intends to put on an "antic disposition" after talking with the Ghost and finding out the supposed truth of what happened to his father. Certainly he is under lots of pressure, but there is enough evidence to make me doubt that Hamlet is mad.
I agree also that Hamlet is not crazy. He is disturbed. He is disturbed because he has to choose between his mother and his father. This is the crux of his dilemma.
If he honors his father by revenging his father's death, he will be killing his mother's husband and destroying her happiness. If he chooses to honor his mother's happiness, he will be letting his father's death go unpunished.
There is a great weight in his decision.
I don't think we can look at the ghost scenes as being evidence of Hamlet's madness. We have to look at them instead as narratively essential moments, without which Hamlet's decision would be much less clear and therefore less dramatic.
I'll agree. I don't think he really is crazy (although it's pretty hard to define that term, right?). I think that he is too aware of what he is doing and too able to make plans at pretty much every point in the play for him to truly be insane.
There are places in the play where he shows extreme melancholy over all of the troubles of his life, but I would argue that he is not actually mad. The most obvious place to start with this question is the fact that he tells Horatio and the others that he is going to "put an antic disposition on." He directly says he is going to act mad and even goes on to demonstrate the kinds of things he is going to say and do in his pretend madness. In the subsequent scenes, he acts oddly and alarms everyone at court, but he is clearly in command of his senses. He makes pointed jokes; he plays off peoples expectations of him; and he continues to logically plot against Claudius.
I get the feeling that he's given up on civil behavior because it doesn't get you anywhere; you can be the best son in the world and a prince favored by the people, and your mother still marries your uncle six weeks after your father died. Hence where most people, like Horatio, would be tactful or reasonable or just keep their mouths shut and defer action, Hamlet belittles, mocks, quibbles, and generally dances on the border of what is considered civil and reasonable.