Thavian in Ash And Cinders. It's like the fantasy equivalent of Gene Wilder's Willy Wonka. He noticeably limps across a frozen river, and once he's got everyone's attention, he throws his wolfskin cloak and staff aside, and the first thing he does is "a wordless, gleeful cry" before conjuring up a whiskey bottle.
The Rock Lord, in its first appearance, is given a descriptions similar to the Great Goblin in the Hobbit. Its first act in the story is to grab a Stonewight by the throat and hammer him alive into a brutish sword. Turns out, that's where all its Evil Minions get their weapons.
The headmistress, Dr. Elizabeth Carson, gives the welcome speech and immediately comes across as someone you'd better not cross. Then later on, at Halloween, we meet her other identity, Lady Astarte, and we find out she's really someone you shouldn't tick off.
Trevor James Goodkind is a Sheltered Aristocrat, heir to billions in a wealthy anti-mutant business family and being groomed to be one of the Goodkinds who takes over the reins of power. We first see him and his family at dinner, being waited on, having a staff of chefs, and Trevor is plotting about how, when he grows up, he's going to get his favorite chef to come with him when he moves out. The next morning, he manifests as a mutant and things rapidly go downhill from there, with a series of Break the Haughty scenes.
The first episode of The Guild is just a long string of these for each of the characters, first establishing Codex with her weblog:
Codex: So, it's uh Friday night, and...still jobless, yay. I haven't left the house in a week. My therapist, uh, broke up with me. Oh yeah, there's a, there's a Gnome Warlock in my living room, sleeping on my couch.
In Dream High School, most of the characters have one very soon after they're introduced.
Corliss' second line:
She gasps excitedly. "You're from Central High, right?!"
One of them tenses, his shoulders shooting up. He turns around slowly, his face downturned but eyes glaring up at Corliss'.
Nara, when she gets Corliss off your back:
"Hey, no problem, that's what best friends are for! I can tell you're stressed out."
When Micah explodes on Page 14:
"Look, you don't even have any friends besides Nara, and all you do is hole up with her in this house! You need to get out there and make more friends, and here's the perfect, lowest-risk opportunity to do it! You're a loner, a loner! And you've been this way ever since Mom died, and I'm-" he uses a passion word I never thought he'd use- "sick of it!"
Principal Wyatt, when she talks to you about the dream scenery on page 24.
When Iris leads the group of actors your way on Page 27.
"Iuh- saw you swoop in yesterday night. THAT was funny! Uh, anyway, you'll probably be joining US! WE'RE THE DWARRVES!"
Aidan tries to bug you as soon as you meet.
Aidan gets in my face with a giant smirk: "Jiiiiiiiii-dooooooooww? Or do you prefer to go by 'Grok'?"
When he first appeared, Montoya initially came off more or less seemed just another petty crook looking for money, acting casual and occasionally joking with his partners. However, the brief glimpse into his personal life and his subsequent calling out of his own partner for refusing to tip a waitress quickly showed how likeable a guy he really was and turned him into an Ensemble Darkhorse.
Rotor probably got his establishment as a rough and cold-minded but extremely competent leader when he lead the initially assaults on the XERRD Fortress, considering he got to show off his talents rather nicely.
Cabin's introductory scene more or less established her as a realist, though she had a few later moments that showed off another side.
Pharisee arguably got his when we first met him, coldly looking over the case files of several controversial individuals and judging them each harshly. It certainly sets up several things, among them his brutal beat down of Montoya.
Unintentionally subverted with Trigger, whose introductory scenes attempted to establish him as a badass and an expert in the Maelstrom, but only caused people to see him as a complete Jerkass and an idiot.
Sarah Bishop's rather violent No-Holds-Barred Beatdown of Rotor, not to mention bludgeoning Cabin in the face when she tried to break it up should give you a pretty good idea of her mental state by this point.
The Red Guy's first line in Don't Hug Me I'm Scared series is "That sounds really boring," after Sketchbook says that they use their hair to express themselves. This sets up his general lack of enthusiasm and inflection throughout the next six episodes.
In Wolf 359, Isabel Lovelace arrives on-board the Hephaestus in a radioactive, homemade spaceship, carrying an empty gun containing a hidden audio recorder, with a bomb wired to her pulse, set to explode should her heartbeat go too fast or stop.