Antagonist

Claudius

Claudius kills Hamlet's father and then makes repeated efforts to murder Hamlet himself. He's also helped himself to Old Hamlet's wife and crown (which was supposed to go to young Hamlet). It's pretty clear that he's the antagonist.

Hamlet

No, that's not a typo. Hamlet is not only a "Protagonist," he's also his own worst enemy. All that thinking, feeling, and brooding about his father's murder and his mom's sex-life gets in the way of Hamlet's quest for revenge. So, maybe it's more accurate to say Hamlet's brain is an "Antagonist" in the play.