Hamlet, Prince of Denmark
If this were a typical Hollywood movie, Prince Hamlet would have avenged his parents' deaths and gone on to enjoy a glorious reign as Denmark's brand new king. However, because this is an adaptation of Shakespeare's longest tragedy, nothing quite so edifying happens to the protagonist at the end, and like most of the characters, he is murdered. Hamlet is a loyal son who is grieving for his father, and does not want to be hurried along in his mourning. He is also a respectful son and when his father's ghost appears to him, he knows that he has to pay attention to it, but he is also a realistic young man, and unsure whether ghosts are a wholly reliable source of information.
Hamlet is romantically interested in Ophelia but is not the type to go mad with love and by the time she rejects his attention he is more focused on proving that Claudius killed his father than he is on winning her back. He is a skilled tactician and also very good at reading people; it does not take him long to realize that his two visiting friends are working as spies for his uncle.
In the end, Hamlet is victorious in the sense that he manages to avenge his father's death and reveal Claudius as a murderer, but he is also killed himself, which is what makes the story tragic.
King Hamlet's Ghost
Prince Hamlet's father has recently died, and he wants Hamlet to know that it was his brother, Claudius, who murdered him. Claudius has taken everything from him including his life, and he wants his son to avenge his murder. He appears only to those whom he believes will be receptive to achieving this end, which is likely why his wife, Gertrude, is unable to see him.
Claudius
Claudius is a man with no principles. He has murdered his brother, taken the kingdom for himself and also married his brother's widow after an extremely short courtship. He has also managed to turn her against her son, whom he does not like, and whom he believes is the only person able to see him for the person he really is, which makes him dangerous, and also means that he needs to be removed from court by any means necessary.
Claudius considers himself a master manipulator and so when he involves Rosencrantz and Guildenstern in his machinations it does not occur to him that his nephew will realize it. He is fairly easily outwitted and ultimately he is killed by Hamlet when his plot to murder him does not only that, but kills the entire royal family as well.
Queen Gertrude
King Hamlet's widow is easily distracted from her grieving by the attentions of her brother in law, whom she marries after an indecently short period of time. She is loyal to Claudius and unable to see his true colors, which precipitates discord between her and Hamlet, whom she begins to believe really is going mad, a belief that is reinforced when she witnesses him talking to his father's ghost, whom she cannot hear or see herself, and therefore assumes that he is starting to have conversations with people who are not actually there.
Gertrude is happy to see her son doing so well in the fencing contests and so drinks a toast to his honor, unaware that the wine she is drinking is a sort of Plan B for killing Hamlet, and she dies as a result of poisoning.
Polonius
Loyal and long-tenured adviser Polonius is the father of both Laertes and Ophelia. Laertes is jealous of Hamlet and does not like him very much but Ophelia is smitten with him, a fact that irritates her father and also concerns him given that his intention is to stay on the right side of Claudius and help him wherever possible. Polonius is instrumental in his daughter's death because he forbids her to see Hamlet, which sends her mad with grief. He is killed by accident by Hamlet when he tries to restrain him during a confrontation with Gertrude, and Hamlet assumes him to be Claudius.
Ophelia
Beautiful and emotionally delicate, Ophelia is smitten with Hamlet and would like to marry him, and so is devastated when her father and brother both tell her to have nothing to do with him. She gives back his love tokens because she is instructed to, but this seems to bring more grief to her than to Hamlet in the end. She wanders the castle grounds, going steadily madder, until she hears of her father's death which sends her beyond the brink of insanity. She drowns but nobody is certain whether is was in the grip of madness or whether she committed suicide.
Laertes
Polonius' son is firmly in the pro-Claudius camp at the castle, mainly because he seems to be a confidante of the king, and because he also gets the rather special treatment that one would think would be reserved for Claudius' grieving nephew. Laertes spends much of the first part of the movie at school in France, but when he returns is central to the tragedy that unfolds. He wants to avenge his father's death just as much as Hamlet wants to avenge the murder of King Hamlet, and so is a very willing participant in the duel. He is not as good a fencer as his opponent though, and has to resort to abandoning the rules completely and stabbing wildly at Hamlet. He is killed with the poison-tipped end of his own foil when the scuffle causes both men to drop their weapons and pick up the foil belonging to their opponent.
Rosencrantz and Gildenstern
Visiting from overseas, Rosencrantz and Gildenstern are supposed to be Hamlet's friends, but it's hard to believe that when they are so willing to plot against him with his uncle. They are theatrically inclined and bring with them a troop of actors who become instrumental in proving Claudius' guilt in the murder of King Hamlet. They are ultimately killed when Hamlet pulls off an elaborate bait-and-switch on the way to England.
Horatio
Horatio is a loyal friend and sees Hamlet more like a brother than a friend. He sees King Hamlet's ghost before Hamlet does, and immediately tells him of this vision and what he believes to be the reason for it. Hamlet believes him without questionning his motives, which speaks highly of his moral fortitude and the reliability of his friendship.
Horatio remains true to Hamlet for the entire movie, the only character to do so. He is the last man standing at the end of the story, which distresses him enormously because he cannot conceive of living in a world that does not have Hamlet in it; however, as Hamlet dies in his arms, he begs him to remain alive so that he can take over the throne of Denmark.
Fortinbras of Norway
Prince Fortinbras arrives at the castle as a courtesy, in order to thank Claudius for allowing his troops to travel through Denmark on their way to Poland; however, when he arrives he realizes that the entire Danish royal family has been killed, and he sees this as an opportunity to claim the throne for himself without having to engage in any battle whatsoever.
