Hamletguide.com | Hamlet's Characters: Hamlet

Wikipedia says:

Claudius is shown at the beginning of the play to be a capable monarch as he deals diplomatically with such issues as the military threat from Norway and Hamlet's depression. It is not until the appearance of King Hamlet's ghost that it is revealed that Claudius may have poisoned the old king in his sleep in order to usurp both his throne and his wife. During the play's progression he takes a turn for the worse by first resorting to spying, and, when that fails, murder.

It is in Act III scene 3, when Claudius forestalls Hamlet's revenge by confessing his sins to God in his own private chapel, that the audience can be sure of his guilt. He is shown to be discontent and unhappy with the events taking place. The young prince spies him brooding about his wrongdoings and trying to pray for forgiveness, but he knows all too well that prayer alone will not save him if he continues to benefit from his own sin. If he was to truly repent, he would have to confess his sin and give up all he achieved through it, which he chooses not to do. Despite his remorse, the King still seeks Hamlet's death in an effort to save both his throne and his life, as he believes the prince is now aware of his part in Old King Hamlet's death. Hamlet is ready to kill him, only to back down, feeling that to kill the King in such a way would contradict the revenge conditions given to him by his father, who commanded him specifically: "Taint not thy mind."

When Laertes seeks revenge for his father Polonius's death at Hamlet's hands, Claudius finally concocts a 'surefire' plan to deal with Hamlet once and for all. He arranges a fencing match between Hamlet and Laertes, but plots with Laertes to poison his foil and give Hamlet a poisoned drink. The king's plan fails; Queen Gertrude drinks from the poisoned chalice instead of Hamlet and dies, and Hamlet, after being struck by the poisoned foil, captures the same sword and strikes Laertes. As Norway's army, led by young Prince Fortinbras, surrounds the castle, Hamlet finally exacts his revenge and slays the king by stabbing him and then forcing him to drink the very poison that Claudius had intended for Hamlet.

Sparknotes writes:

Hamlet’s major antagonist is a shrewd, lustful, conniving king who contrasts sharply with the other male characters in the play. Whereas most of the other important men in Hamlet are preoccupied with ideas of justice, revenge, and moral balance, Claudius is bent upon maintaining his own power. The old King Hamlet was apparently a stern warrior, but Claudius is a corrupt politician whose main weapon is his ability to manipulate others through his skillful use of language. Claudius’s speech is compared to poison being poured in the ear—the method he used to murder Hamlet’s father. Claudius’s love for Gertrude may be sincere, but it also seems likely that he married her as a strategic move, to help him win the throne away from Hamlet after the death of the king. As the play progresses, Claudius’s mounting fear of Hamlet’s insanity leads him to ever greater self-preoccupation; when Gertrude tells him that Hamlet has killed Polonius, Claudius does not remark that Gertrude might have been in danger, but only that he would have been in danger had he been in the room. He tells Laertes the same thing as he attempts to soothe the young man’s anger after his father’s death. Claudius is ultimately too crafty for his own good. In Act V, scene ii, rather than allowing Laertes only two methods of killing Hamlet, the sharpened sword and the poison on the blade, Claudius insists on a third, the poisoned goblet. When Gertrude inadvertently drinks the poison and dies, Hamlet is at last able to bring himself to kill Claudius, and the king is felled by his own cowardly machination.

The present King of Denmark and Hamlet's uncle. He succeeds to the throne by murdering his brother and incestuously marrying his sister-in-law. He is devious and manipulative, except for one moment of fearful regret.