Hamlet/Characters

Alternate Character Interpretation is applicable to pretty much everyone here.

Adult Child: If he is indeed 30 (see writers can't do math), he very much qualifies.
Anti-Hero: Type IV
Byronic Hero: Borderline example, but fits.
Deadpan Snarker: Immensely so.
The Ditherer: His Fatal Flaw, according to many critics.
Double Entendre: Fond of making these, especially around Ophelia.
Emo Teen: In the productions where he really is a teenager, at least.
Hidden Depths: Still hidden to this day, in fact.
Jerkass: At his worst...which is often.
Kill Him Already!
Lost in Character: One possible interpretation of the character.
Mommy Issues
Mood Swinger
Obfuscating Insanity
Pungeon Master: An uncommonly melancholy master, but every other word out of his mouth is a Double Entendre or Stealth Insult.
Sword Over Head: Ironically, things would have worked out much better if he had taken the opportunity.
Tragic Hero
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

Big Bad
Boisterous Bruiser: Sometimes played this way.
Casanova
Dirty Coward
Dirty Old Man: How Hamlet sees him.
Evil Prince
Evil Uncle
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.
It's All About Me
Manipulative Bastard
Not So Different: His actions and those of Hamlet, specially regarding the letter to England, are rather similar.
Rasputinian Death
Succession Crisis
Villain with Good Publicity: Seems this way at first, especially to Hamlet.

Break the Cutie
Brooding Boy, Gentle Girl: Hamlet and Ophelia could be seen as a deconstruction.
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.
Flower Motifs
Kill the Cutie
Love Hurts: Especially for the love interest in a Shakespearian tragedy.
Mad Oracle: Possibly in her mad scene.
The Ophelia: The Trope Namer.
Star-Crossed Lovers: At least as far as her father is concerned.
Talkative Loon
Temporary Love Interest

Anti-Villain: Types II and III.
Big Brother Complex
Brother-Sister Incest: Implied in some productions.
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.
Dead Little Sister: Ophelia
Defeat Means Friendship: With Hamlet
Foil: For Hamlet, who lampshades it.
Hoist by His Own Petard: Killed by the same poisoned blade he uses to kill Hamlet.
Hot-Blooded
My Sister Is Off-Limits
Redemption Equals Death
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.

Brevity Is Wit: While one of his lines is the Trope Namer, Polonius himself averts his advice to spectacular effect.
Captain Obvious: His Last Words, if anyone was unsure.
The Consigliere: Certain interpretations see him even as The Man Behind the Man regarding Claudius
Idiot Ball: Takes it and runs with it.
Lack of Empathy: He may try to look like he has empathy, but would anyone who has empathy try and test if a relationship is real by making his daughter pretend to dump the guy?
Love Makes You Crazy: Abides by this philosophy regarding Hamlet and Ophelia.
Obfuscating Stupidity
Overprotective Dad
Purple Prose: His standard manner of speaking, played for laughs with the advice given to his son, as well as the trope naming line for Brevity Is Wit.
Wrong Genre Savvy: Seems to think he's in a Star-Crossed Lovers play rather than a revenge tragedy.

Christmas Cake: When an actress is past her prime, she is said to be "playing Gertrude" (ie: rather than Ophelia).
Parent with New Paramour

The Ace
Foil
Hot-Blooded
Only Sane Man: Out of the Hamlet/Laertes/him trio, he's the only one that gets things done and doesn't end up dead.