The most obvious answer to this question is his death by both sword and poison at the end of the play, Act 5 scene 2. But I think you could also examine other smaller ways he is punished for his misdeeds before that final act. Claudius killed and his brother to take the throne and married his sister-in-law in what most would have considered an incestuous marriage. These acts are not taken lightly, even by Claudius who could seem to have no conscience. In Act 2, Polonius remarks that people sometimes "sugar o're the devil himself." He is only referring to people putting on an act sometimes, but Claudius mutters in an aside, "How smart a lash that speech doth give my conscience." This reveals that he IS bothered by his conscience and feels some measure of guilt. During Hamlet's play-within-the-play, Claudius feels guilty and commands that the performance end and the lights be brought up again. This is EXACTLY the guilty reaction Hamlet was looking for, and now Claudius is punished again with his guilty and conscience, and the added concern over what Hamlet is going to do with this knowledge. Claudius spends the rest of the play in a state of controlled panic, trying to keep control of his situation. He plans to send Hamlet to England to be killed there, but he has to pretend to care about Hamlet in front of Gertrude so that she doesn't suspect anything. When Laertes returns to Elsinore looking for vengeance for Polonius's death, Claudius must talk him down from hurting him, and then work hard to convince Laertes that it is Hamlet who deserves the blame. When Claudius receives the note from Hamlet that Hamlet has in fact returned from England and is in hiding, he has to be in a state of worry about what Hamlet is going to do and when, all while maintaining a calm and cheery front to the everyone at Elsinore. Claudius lives a state of high anxiety, and that is part of his punishment. His ultimate punishment is when the plot used for Hamlet is turned around on him. The poisoned sword and cup were intended for Hamlet, but ultimately are used against him, and as Laertes says, he is "killed with [his] own treachery."