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. (The crown, not the wife. It's not that kind of tragedy—or is it?)
In either case, it's pretty clear that Ol' Claud is our antagonist.
Well, obviously. Hamlet is seriously 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. In fact, Hamlet admits it: he says "Hamlet is of the faction that is wrong'd;/ His madness is poor Hamlet's enemy" (5.7). Sure, the madness is alleged—but he still seems to think he's at war with himself.