Byronic Hero: Angsty, thoughtful, cynical, lonely, weary of the world, arrogant, loved by many yet an outcast in his own family, overly dramatic and emotional in some interpretations, filled with self-hatred - Hamlet fits all the criteria to a T.
Deadpan Snarker: Immensely so. Hamlet rather enjoys running circles round Polonius, Rosencrantz and Guildenstern, who are too dense to realize that he's mocking them.
Fatal Flaw: It's widely agreed that Hamlet has onenote he discusses the concept in an early scene. There's rather less agreement on what, specifically, it is.
Hair-Trigger Temper. While his uncertainty is often cited as his key flaw, Hamlet can sometimes surprisingly lash out at people and commit violent acts with little provocation. Most notoriously, he kills Polonius when he mistakes him for the king, hiding behind the arras.
Honor Before Reason: One of his many inner conflicts. For example, when he has a chance to kill Claudius, he does not do so because he fears sending him to heaven. Some critics have identified the additional conflict of pagan values (e.g. family honour, avenging ones father's death) vs. Christian ones (not committing murder, the Divine Right of Kings, etc.).
Hypocrite: He advises the players to resist theatrics and appears to revere passionate people like Fortinbras, but he seems to like grand gestures like the play within a play and is unable to act on his passionate impulses.
Jerkass: At his worst, he can be quite terrible towards the people he interacts with, and his words are cutting. Case in point - his mocking of Polonius, Rosencrantz and Guildenstern, as well as his tirades towards Ophelia and Gertrude.
Jerk with a Heart of Gold: Possibly. In a way, he may have been warning Ophelia of the dangers associated with loving him, rejecting her so that no further harm would befall her.
Karma Houdini: Sort of. He kills Polonius, and although Claudius tries to have him killed on the quiet Hamlet evades punishment. He also seems to receive no punishment for the deaths of Rosencrantz, Guildenstern OR Ophelia, until the very end, and it's implied that Laertes's forgiveness absolves him completely.
Kill Him Already: The driving conflict of the plot is Hamlet's uncertainty and hesitance in avenging his father's death. This may be seen as a more general metaphor for man's uncertainty of his moral duty and place in the universe.
Large Ham: His bragging contest with Laertes over their love for Ophelia - Hamlet's surpasses the love of "five thousand brothers" in its intensity.
Also with Fortinbras. Hamlet realizes this, as well. The four sons Fortinbras, Pyrrhus, Hamlet and Laertes are bound by the same task, yet how differently they approach it is rather interesting to see. (And Hamlet wasn't too bad; Fortinbras delayed for sixteen years.)
Obfuscating Insanity. Many in the court (particularly Polonius) perceive Hamlet's eccentric speech and behaviour as signs of madness. It is up to the director's and audience's interpretation as to how much is feigned (to put Claudius in a false sense of security) and how much is real.
Odd Friendship: With Horatio. The Prince of Denmark, best friends with a commoner he'd met in college? Not to mention their contrasting personalities.
Tragic Hero: Hamlet's story is, superficially, a classic revenge tragedy, a very popular genre at the time. In more general terms, Hamlet may be seen as the tragic representation of man as an individual, torn between a search for truth and an immediate duty, between fate and free will, between one moral code and another, whose uncertainty and hesitation leads to his downfall.
Tragic Mistake: Hamlet's downfall can be traced back to the moment where he sees Claudius at prayer and decides to wait until later to avenge his father.
Writers Cannot Do Math: Leading to problems with calculating his age. While he is a student (which at the time wouldn't have put him past his late teens or early twenties), the gravedigger indirectly mentions that he is about thirty. Real-life casting issues may have played a role here.
You Killed My Father: Hamlet's main motivation is to avenge his dead father. His desire to establish absolute certainty and to kill the usurper under exactly the right circumstances leads to much delaying, and ultimately the death of most of the Danish court.
Comforting the Widow: Claudius "comforts" Gertrude. It helps win him the throne. On the other hand, he does seem to genuinely love her. It is not an unpopular Alternative Character Interpretation that the throne was an afterthought and Claudius killed the king solely for Gertrude.
Ignored Epiphany: Actually comes close to repenting at one point, but he can't make himself give up the kingdom. Instead he gives up any thoughts of atoning and just concentrates on being King.
No Name Given: In the play itself he is never named, everyone calling him "The King", "Your Uncle" or "My Husband".
Not So Different: His actions and those of Hamlet, specially regarding the letter to England, are rather similar.
Sibling Triangle: Claudius murders his brother and marries his brother's wife. Interpretations vary as to how complicit Gertrude is in the plot.
Disposable Love Interest: She's completely passive and entirely defined by her relationships with the male characters. When they all disappear (Hamlet rejects her, her father dies and Laertes is abroad) she goes completely to pieces and commits suicide.
Does Not Like Shoes: In many adaptations — theatrical productions, films, paintings, etc. — Ophelia is barefoot during the mad scene.
Driven to Suicide: Probably, unless she was just so insane she didn't take heed to her clothes soaking up water while lying in a river. This is all, of course, open for debate.
Neutral Female: She shows very little independence and simply acts as a pawn to her father, and then as then motivator for Laertes' revenge after her death.
Speech Impediment: In certain interpretations, Ophelia does have a lisp, and some of her lines actually reflect this (for example, "twice two months" is understood as "two-es...two months). This gives Hamlet's line ("...you lisp, you nickname God's creatures...") a second, literal meaning.
Anti-Villain: While he sides with Claudius in conspiring to poison Hamlet, his motivations in doing so are thoroughly understandable. His desire to avenge his father and sister is no different from Hamlet's goal of avenging the dead king.
Big Brother Instinct: Before leaving for France, Laertes warns his sister Ophelia from getting involved with Hamlet.
Chekhov's Gunman: He is introduced in the first act and appears briefly in two scenes before departing for most of the play. He returns to play a major role in the final act.
Death Equals Redemption: Only when he knows he is dying does Laertes reconcile with Hamlet, absolving him of his father and sister's deaths and urging him to kill Claudius,
Defeat Means Friendshipnote Or rather: Mutual Kill Means Friendship: When it is clear that they are both dying, he and Hamlet reconcile and he reveals all of Claudius' plot. This knowledge of his impending death is the final impetus that Hamlet needs to carry out his revenge.
Foil: For Hamlet, who Lampshades it in the final scene. Both seek to avenge their fathers' deaths, but while Hamlet is extremely cautious to establish his uncle's guilt, Laertes almost commits regicide based on nothing but a hunch.
Hot-Blooded: He re-enters the play in Act IV in a rage over the death of his father, and comes very close to killing Claudius. He later brawls with Hamlet in his sister's grave, despite having already agreed to a more formalised duel.
You Killed My Father: His reaction to his father's death stands in stark contrast to Hamlet's behaviour. While Hamlet's hesitation to seek revenge proves to be his undoing, Laertes is quite the opposite. After hearing that Polonius has been killed, he immediately jumps to the conclusion that Claudius is responsible. He returns to Denmark with an army of supporters, bent on committing regicide.
Abusive Parents: Certain interpretations of Polonius show him as this towards Ophelia, manipulating her and keeping her emotionally stunted.
Berserk Button: Fairly meek and submissive for most of the play but insulting or threatening Claudius will make her go Incredible Hulk on your ass. "Oh this is counter you false, Danish dogs!"
Christmas Cake: When an actress is past her prime, she is said to be "playing Gertrude" (ie: rather than Ophelia).
Guess Who I'm Marrying?: Hamlet is deeply shocked that she marries her former brother-in-law so soon after her husband's death.
Heroic Sacrifice: Some interpretations hold that she knowingly drinks the poisoned drink intended to kill her son.
Parent with New Paramour: She marries Claudius after the elder Hamlet's death. Whether or not she was complicit in the murder varies depending on interpretation.
Karma Houdini: Arguably - some readings of the text and some adaptations have him attempting to conquer Denmark underhandedly rather than just passing through with his army as he claims, and the ending for him is Hamlet supporting him to be the next king. If this was his plan, then he's not only not made to pay for his treacherous actions, he ends up being rewarded for it.
Ho Yay or Heterosexual Life-Partners: He and Hamlet seem quite close, to the point of Horatio being willing to commit suicide upon Hamlet's death (effectively forsaking his own salvation). Horatio is the only person Hamlet truly trusts enough to impart his plans to him, the only one who doesn't betray him in some fashion. Some productions do add a homoerotic element to their relationship (or, in one case, they cast Horatio as a woman in love with Hamlet).
I Should Write a Book About This: Hamlet commands him to keep his memory alive after he is dead, and it is implied that Horatio becomes the narrator of the story.
Morality Pet: Probably the only person Hamlet is consistently nice to.