Conspiracy and Plotting
From the very beginning of the play, the key theme is the art of conspiracy and the plot consists of one group of characters after another plotting the downfall of their perceived enemy. This can be political, such as the diplomatic conspiring that goes on between Denmark and Norway, whose Crown Prince is plotting against Denmark because his father was roundly beaten back by them in a recent battle; it can also be personal, as in the case of Laertes, who is plotting with Claudius to kill Hamlet because he blames him for the deaths of his father and sister.
Claudius has taken the throne for himself as the result of his plotting; he plotted the murder of his brother and the seduction of his widow shortly thereafter. Now, a perceived threat to his status quo in the form of Hamlet prompts him to plot the murder of his nephew as well. In order to carry out this murder, he conspires with Polonius, Rosenzrantz and Guildenstern and Laertes in order to put his plan into action.
Hamlet is also conspiring and plotting, primarily with Horatio, whom he trusts, but also with the sentries who have seen his father's ghost. Their conspiracy involves Hamlet's pretense of madness. The theme throws up some thematic ethical dilemmas; for example, Hamlet is trying to find out who murdered his father, so can his plotting really be considered an unethical thing? The play shows that it is not the act of conspiracy in of itself that is unethical but the reasons and motivation behind it.
Tragic Love
Hamlet and Ophelia are in love with each other and left to their own devices would likely get married, but like Shakespeare's other tragic protagonists Romeo and Juliet, their love is doomed because their families cannot prevent themselves from getting involved in it. Neither Claudius nor Polonius cares about the feelings of the young people concerned; Claudius is merely concerned with eliminating Hamlet and Polonius wants what is politically expeditious to him rather than what might make his daughter happy. Ophelia is forced to return Hamlet's love tokens and letters, which leaves her so distraught that she descends into madness and kills herself by drowning herself in the lake.
Hamlet is so in love with Ophelia that he is prepared to reveal his hiding place whilst her funeral procession goes by at the gravesite. In a play that is so filled with "fake" emotions and ill-will towards each character, this relationship is one of the few that is genuine and rooted in goodness.
Oedipal Relationships
Although the issue of incest is not emphasized too much in this film, there is a sub-theme that centers around the inappropriateness of some of the relationships between the characters. Perhaps the most glaring example of this is the relationship between Ophelia and Laertes, at least from Laertes' side of the relationship. He seems inordinately interested in his sister's romantic life, and seems jealous of Hamlet not in a protective way, but in the way that a man might be jealous of a rival in love. He also uses highly sexualized language to and about his sister. The fencing match between Hamlet and Laertes is almost a match to win the hand of the fair lady as much as it is a match to avenge the honor of each man's father.
Hamlet is also rather sexual in the way that he talks to and refers to Gertrude, his mother. When he realizes that Claudius has killed his father, he does not urge her to leave the marriage, just to stop sleeping with her husband. He is preoccupied with Gertrude's sex life and also seems attached to her in a way that is more that of a lover than a son.
Death and What Comes After
The play is essentially about a murder, and it also revolves around a succession of other murders. This makes it heavily focused on the subject of death. Almost all of the main characters in the play are dead by the final act. Hamlet himself is preoccupied with death and also what comes after it. He is confused by the afterlife, and his reason for living is not so much for love of life, but for uncertainty and fear of death.
When Yorick's skull is revealed by the grave diggers, it prompts Hamlet to ponder the nature of life and death, and to observe that death is a great equalizer because it comes to everyone, and everyone, from the richest to the poorest, will end up in a grave like Yorick's. This propensity to dwell on the nature of death makes Hamlet a melancholic character.
