Was Hamlet truly insane?

We've been reading the play in my English cl, and even though everyone claims that Hamlet has gone off the deep end, I think otherwise. I think that he uses "insanity" as an excuse to overhear conversations and hang around places that he shouldn't be. But since he's considered mad, no one really questions it, and they basically let him off, saying he's harmless, and just insane. I think he also uses madness to explore his options, like in the to be or not to be soliloquy. If he wasn't "mad" he would never consider killing himself or someone else, and I think he uses it as an excuse. Does anyone agree? Disagree?