Hamlet is the story of how Hamlet, a young prince, contrives to avenge his murdered father. The play is quite simple, accentuated by a few plot twists, but generally a clear revenge-tragedy. All this when lions are overgrown housecats and "Starry Night" is a few splotches of color on a canvas. Why does Hamlet aim to kill Claudius? Certainly, the Ghost has directed him to do so, but does Hamlet have other motivations or even conflicting interests? Such questions are invariably brought up; Freud discussed the Oedipan tendencies of Hamlet in a letter to Wilhelm Fliess in 1897. Therefore, the relationship between Hamlet and Claudius must either have some redeeming value, or Freud and others are entirely too eager in their searches for literary examples for their theories. For the sake of argument, let us proceed from the former.
Claudius is not the object of unmitigated hatred, indeed, Hamlet shows immense trust for Claudius, at least coming into the play. Even further, Hamlet is jealous of Claudius, both in terms of power and more base desires. While arguments might be made for just these two, or even solely the latter of these motives, a third motive seems to appear, that of vengeance and, thence derived, hatred.
In Hamlet's first soliloquy (I.ii.129-59), he shies away from blaming Claudius, instead addressing Gertrude as the progenitor of all that ails Denmark. Soon thereafter, when Horatio arrives, Hamlet again plays her out as the active party:
Horatio: My lord, I came to see your father's funeral.
Hamlet: I pray thee, do not mock me, fellow-student;
I think it was to see my mother's wedding.
In speaking with the Ghost, Hamlet expresses his eagerness to avenge Old Hamlet in I.v.29-31, only to express reluctance for the balance of the play, exemplified by the famous "The time is out of joint. O cursed spite, / That ever I was born to set it right!" (I.v.188-90) When first Hamlet does respond to the Ghost's exposition, he only condemns Claudius after cursing Gertrude ("O most pernicious woman!", I.v.101), and that, too is a surprised response.
102 O villain, villain, smiling, damned villain!
103 My tables,---meet it is I set it down,
104 That one may smile, and smile, and be a villain;
105 At least I'm sure it may be so in Denmark.
Repeating "villain," cursing, generally inarticulate phrasing – this passage is atypical for the eloquent Hamlet, here obviously caught off-guard. He must have placed some faith into Claudius to this point, otherwise there would be no shaking revelation. Hamlet's trust for Claudius is shattered, however, by the Ghost's message, and from that point on, other motives carry Hamlet.
Perhaps the most interesting analyses develop Hamlet as an Oedipan character, building from the previously mentioned letter by Freud, but also supplemented by a recent Kristevan psychoanalysis of Hamlet. By this argument, the remarriage of Gertrude to Claudius has recalled the primitive lust for his mother, as she is restored as a sexual object (Freud 1897). Claudius has supplanted Old Hamlet as the "father," and therefore is the barrier to his mother. In the first soliloquy, Hamlet laments that Gertrude was not more like Niobe, who mourned dreadfully for the deaths of her twenty children (I.ii.49). More importantly, however, Niobe is said to have resisted the incestuous advances of her father, who then put her children to death as punishment. Also noting that Hamlet refers to the relationship between Gertrude and Old Hamlet as nearly that of mother and child, expressed in the juvenile "she would hang on him, / As if increase of appetite had grown / By what it fed on" (I.ii.43-45), we can thence see Old Hamlet as the son killed by refusal to indulge in incest.
There is a distinct lack of clear imperative of action in Hamlet. Hamlet is confused, slightly mad, certainly indecisive. Borrowing from the nomenclature of Aristotle, Hamlet is not of the arete form – composed of an aggregate of qualities, in sum producing a "good" character. He is troubled, but not by any one flaw, so he does not well fit hamartia. Conflicting interests, carnal desires, pressing time, supernatural urgings, all tugged at Hamlet's course. Non-committal to his end, and everyone's end, Hamlet is a tragic non-hero, the exemplary do-nothing who managed to have everything happen.