* King Hamlet: He is murdered by his brother Claudius, who then marries Hamlet's widow, Gertrude. King Hamlet's ghost appears to his son, Hamlet, and reveals the truth of his murder, setting the play's events in motion. King Hamlet ultimately finds peace and is presumably in heaven, as he tells Hamlet that he has been "cut off even in the blossoms of my sin, unhousel'd, disappointed, unaneled."
* Laertes: He is the son of Polonius, the Lord Chamberlain. He is deeply grieved by his father's death, which he believes was caused by Hamlet (though it was actually Claudius's act). He is manipulated by Claudius into revenge, culminating in a duel with Hamlet where both are fatally wounded.
* Queen Gertrude: She is Hamlet's mother and marries her deceased husband's brother, Claudius, after his death. She is unaware of Claudius's crime until later in the play, when Hamlet confronts her. She dies by accident, poisoned by Claudius's plot to kill Hamlet.
Let me know if you'd like more details about any of these characters or any other aspect of the play!