The whole story "The Bikini-Suicide Frisbee Match" serves to establish ZoŽ as the relatively normal person and Chew Toy of the group. It's almost an exaggeration of what she's going to be like, but her being a dump for the consequences of the weirdness in the world of the comic is a permanent thing, even though she learns to deal with it and stand up for herself.
An even more telling moment (well, for those who know Dungeons & Dragons well enough to pick up the implications) comes two strips earlier, when a goblin attempts to incapacitate Belkar with an Evil-aligned spell...and it doesn't affect him.
Xykon has a few in the Start of Darkness origin comic. One is when a Professor Xavier expy visits him and wants to teach Xykon how to use his sorcery powers to protect a world that hates and fears him; Xykon isn't interested and so electrocutes and zombifies the man and sics him and Xykon's zombie grandmother on his parents.
Another moment comes when he reveals to Redcloak he knew in advance of Right-Eye's plan to betray Xykon, and had protected himself against it. The reason he didn't stop Right-Eye was to see if Redcloak was loyal enough to kill his brother to protect Xykon; he then brings the moment home with an Eviler Than Thou speech about how he doesn't need any sort of justification for being evil, destroying Redcloak's will to resist in the process.
His first one is on the first page. Little boy Xykon is crying over his dead dog Barky, then a burst of magic causes the dog's corpse to zombify and eat a bird's brain. Lil' Xykon's reaction? "That was so COOL! C'mon, let's go find some more birds!"
When Elan's father, Tarquin shows up, he gives a long, eloquent explanation for recent events to Elan, and ends with the line, "I am your father," as a Shout-Out to Star Wars. Then immediately enthusiastically yells "Oh MAN! I've always wanted to say that line!" Which establishes him as a very Genre Savvy character that exists to make the fourth wall cry.
The moment Tarquin tells a woman who rejected him earlier that he had her husband killed in battle before having her locked up so she'll be more amenable when he asks her to marry him later pretty much kills any idea that he's a Noble Demon type of villain.
Kharisma's first appearance has her screaming in revulsion at Davan's "ugliness". The next strip establishes she is that shallow. It takes at least twice as much Character Development as Mike's for her to grow out of this. As well as a trip to the slammer and a visit from a little blue dream thing...
8-Bit Theater did this with almost everybody. Especially Thief, Red Mage, Garland, Vilbert...
Funnily enough, this wildly contrasts with his first appearance in Cuanta Vida, in which he ambushes Blue Spy when having a shower. His establishing character moment is a few pages later, when he claims that he was just "testing his reaction", before elaborating on his relationship with the Blue Sniper in very explicit detail.
Spacetrawler: The humans all reveal something about their personality in their first appearance:
Martina is feeling ennui over being "common", and hoping that an adventure is out there somewhere for her. When given a choice to join Interplanet Amity, she jumps at the call.
Pierrot is riding in a car, and he punches the driver for deliberately running over a mole, and the car crashes as a result. Thus establishing that Pierrot really cares about animals, and that he has a tendency to act impulsively on his principles.
Yuri is chatting on the internet when Nogg arrives, and the posters on her wall indicate that she's a well-rounded geek. She joins Interplanet Amity because she wants to see alien technology, and she eventually becomes a cyborg.
Dustin is introduced by brandishing a shotgun at Nogg and threatening to turn him over to the government. This establishes that he's annoyingly loud and xenophobic, and foreshadows his dangerously uncritical trust in "the government".
In General Protection Fault, Trudy is initially smiling through her entire interview, but when Dwayne is away, and Ki feels like she shook hands with the devil, Trudy tells her that she has that effect on "inferior life forms". Soon afterward, Trudy is shown kicking a dog.
The Wulfenbachs in Girl Genius. The baron is menaced by someone with a giant robot. What does he do? Leave his son handle it as an exercise. Said son gives a complete exposition of the situation, direct troops to suppress the dangerÖ Then when a bomb is thrown in his direction, he send it back while protecting both the young assistant (our heroine, actually) and the goldfish. Establishing Character Moment Of Awesome.
Vriska is introduced by mindcontrolling a guy into jumping off a cliff.
Likewise, Meenah's very first action on-screen is to try and kill Roxy for the heck of it.
Gamzee's first appearance involves him rambling aimlessly about miracles and wondering why faygo hisses or how computers work, and yet showing genuine kindness and friendship towards Karkat.
Skin Horse: In the first strip after the prologue, an unarmed Tip Wilkins is facing down an intelligent, deranged, genetically-augmented lion. While wearing a girl's sweater and a skirt. He points out it's a Roberta Frost, because his crossdressing is that important to him. Even when he's on the clock.
Tip: The situation is under control. I'm a psychologist.
Sire: With a heavy Ensemble Cast of characters based off of literary classics the author likes to make each important character have a bold entrance. Susan, the Hyde-Child, is first seen ripping the head off of a doll to torture her Jekyll-Child sister. Riley, The Invisible Man pretends to be a ghost and scares the heck out of the main characters and Emile, the Javert-Child punches a teenage woman in the chest for punching her sister.
Several of the villains in Goblins are introduced this way:
The prologue is an extended ECM moment for Sarine, in addition to serving as one part of a truly marvelous pair of Book Ends.
Meji's identity as a spoiled but magically powerful rich kid (not to mention Ellis' as Deadpan Snarker) is clear enough from the first look at her room that we get in chapter 1.
Jon's first appearance has him abducting Meji to play the Human Shield trick with, even as he tells her he's not going to follow through with it. Can't get much more Anti-Hero than that.
Sara's wipeout of the Gewehr thugs in the windmill leaves very little doubt that we are talking here about not only a Badass, but an emotionless one with ninja skills (and how).
Even the bad guys get a taste of this, as in his first appearance, Ian practices for his eventual role as a Woobie, Destroyer of Worlds by being a Woobie, destroyer of a library.
morphE introduces Billy Thatcher by having him angrily rant about the other character's stupidity in a dangerous situation and how he would handle the situation better. This is before any of the character sprites have even shown up and sets a precedent for his perceived mental superiority and controlling nature.
Adrestia also gets a very shining example when she refuses to participate in a fight to the death with a teenager and instead offers him a broken floor tile and orders him to kill her so that he doesn't have to die.
Russel arrives on the Island of Doom water skiing on the backs of two alligators. There was a plane, but he couldn't afford a ticket because he spent all his money renting the alligators. This sets the precedent for most of his future behaviour.
Buffalo quickly launches into a lengthy explanation of his nonsensical plan for world conquest the first time he appears. As a bonus, this scene establishes Doctor Von Science as a put-upon voice of reason who is consistently ignored.
Alejandro first appears indignantly berating Russel for calling him "that lady" and spends the rest of the page pontificating on his own magnificence.