In the Stephen King novel The Dead Zone, Greg Stillson (the villain) is introduced as a traveling salesman who is tired of the pathetic existence he's been reduced to. After trying unsuccessfully for a couple of minutes to knock on a prospective buyer's door, he ends up kicking to death a defenseless dog that was barking at him, foreshadowing his true motivations later on in the novel.
The first for the title character. It's made plainer in retrospect, but Harry's insistence he's not a wizard, that he's nothing special, in the face of a giant man tracking him through a raging thunderstorm, knowing his birthday, and giving him a letter stating as much, reveals a certain something about his character.
Voldemort gets one before the series actually begins when he murders Harry Potter's parents.
Draco Malfoy gets one when he and Harry meet in Madam Malkin's. He has no idea he's talking to "The Boy Who Lived", and responds to My Parents Are Dead with "Oh, sorry. But they were our sort, weren't they?"
Hermione Granger introduces herself by speaking very quickly, showing excitement for school, dispensing information others don't know, and — this is key — helping a fellow student who's lost something.
Ron Weasley, meanwhile, is the first friend Harry ever makes his own age (Hagrid being the first friend, period). It sets the tone for their relationship throughout the rest of the series, as Ron's loyalty is one of the things which gives Harry strength.
Molly Weasley is first shown helping Harry, whom she hardly knows, get onto Platform 9 3/4. Later, she scolds her children for treating him like an exhibit.
Also, when Snape first looks at Harry, Snape looks not at the scar on his forehead, which marks him as "The Boy Who Lived," but at Harry's eyes, which are just like Lily's. Snape is instead looking for Lily Potter's son in Harry.
From the first moment we see Luna Lovegood, wearing radish earrings, with her wand stuck behind her ear and reading The Quibbler upside down, it is clear she is a world-class Cloudcuckoolander.
While not his first scene, Gilderoy Lockhart's character becomes clear during his first Defense Against the Dark Arts lesson. He brags about his deeds, gives a pop quiz with all questions about himself, and when the pixies he unleashes prove to be too much he flees, leaving the students to deal with the mess.
In The Philosopher's Stone, the first time we see Alpha Bitch Pansy Parkinson is when she sneers at Parvati Patil for showing concern for Neville, who was recently hurt. That meant that she was going to be a bitch on wheels.
In the first book, King Robert's character is soon established when he asks to go down into Winterfell's crypts to see his dead would-have-been betrothed. It establishes him as a good friend of Ned's, an embittered emotional cripple, and a rather thoughtless husband. He also goes on to describe life in the South. It shows his own lust for life.
Eddard Stark executes a deserter that we know had a perfectly legitimate excuse to run for the hills. It establishes Ned as grimly honorable, and also establishes that the heroes of the story aren't always right.
The man who speaks the sentence should swing the sword. If you would take a man's life, you owe it to him to look into his eyes and hear his final words, and if you cannot bring yourself to do that, then perhaps the man does not deserve to die.
In Tyrion's first scene, he cheers up Jon Snow and gives him some good advice. As Tyrion walks away, Jon notices that his shadow stands as tall as a giant, showing that Tyrion is a better man than his stature or reputation make him appear.
Jaime's scene in which he pushes Bran off the tower shows that he's ruthless and willing to do anything "for love." Within the world, Jaime's past regicide dominates every characters' opinions about him.
Including the reader's. It's only in later books as Jaime shows himself not to be the evil person everyone makes him out to be that the rest of this scene makes sense. Though Jaime pushed Bran off the tower the only reason he was able to do so was because Jaime instinctively saved Bran from falling off the tower in the first place despite knowing that it would be a lot better for him if Bran turned into chunky salsa. So while Jaime might be ruthless, he's also a better person than everyone thinks he is.
Brienne gets two; the first is when Catelyn first sees her, as she wins a tournament against several male knights using a combination of brawns and cunning, and receives no respect or reward at all, with her master even referring to one of the knights she defeated as the better fighter while she could hear him. The second is when she drops a boulder on a ship carrying her allies, in the name of protecting a man she hated, because she'd sworn an oath to. The Kingslayerhimself is impressed with her honour, though that might have been because it was him she was protecting.
During the war that overthrew King Aerys, Stannis Baratheon spent months holed up in his castle while it was under siege and nearly starved to death. His life was saved by the smuggler Davos Seaworth, who smuggled food into his castle by night. What did he do when the war ended? He knighted Davos for his services, and then chopped off the fingers of his left hand (the lawful punishment for smugglers). This establishes Stannis as an unyielding man who always does what he feels is right, no matter who it hurts.
Davos himself is first introduced as Maester Cressen's friend. Maester Cressen is the only person in Stannis's service who sees Melisandre for what she is - except Davos. His brief introduction as Cressen's friend, whose primary goal is to overthrow Melisandre, establishes him as the voice of reason, a genuinely good person, and very much against The Red Woman.
Gregor Clegane losing a joust to Loras Tyrell causes him to go berserk and behead his own horse before his brother Sandor restrains him.
Not behead. Bifurcate.
Theon kicking Gared's decapitated head, and in the same chapter arguing to kill the direwolf pups.
The Greatjon's famous "Your meat is bloody tough" scene.
Jon and Robb, respectively, saw two different things when they looked at the eyes of the deserter their father executed: Fear and Courage.
In Consider Phlebas, the Culture establishes itself as "the ridiculously powerful civilization you don't want to mess with" by having one of its warships jumping Out of a Sun. It's also established by the Idiran commander's claim that any time their ships have faced the Culture's, they lost badly. Later it turns out said "warship" was a diplomatic vessel technically not made for war at all!
Jiriki gets a cool one where he is first encountered strung up in a trap, and when the trap-setters show up he starts fighting and spitting, and as soon as he is freed he proceeds to defeat all of the humans come to find him and acknowledges his debt to Simon for cutting him down while abruptly vanishing into the wood.
In Red Dragon, Dr. Hannibal Lecter's first appearance establishes his almost supernatural sense of smell. "That's the same atrocious aftershave you wore in court, three years ago."
In the sequel, The Silence of the Lambs, he does it again with Clarice's skin cream. Jame Gumb's big establishing moment (after being told lots about his modus operandi by Crawford) would probably be his infamous "It puts the lotion on its skin or else it gets the hose again" scene, at once brutally menacing his captive and cuddling his bichon frise. Also his voice (in the movie, anyway) can't make up its mind whether to be high and effeminate or low and masculine.
In Rogue Squadron, first book of the X-Wing series, Wedge has that entire scene where he walks into the hangar, inspects his X-Wing, compliments his new chief mechanic, and takes off to attend a training exercise. Beyond this trope and providing a vehicle for Stackpole's worldbuilding, there's no point to the scene. It establishes that he's very conscious of his authority, he's good at math, good to his subordinates, aware of what he needs to teach new people, and an Ace Pilot of such skill that his kill silhouettes include two Death Stars, a lot of big ships, and so many fighters that they couldn't fit on the side of his X-Wing, so some had to be rendered in red, representing a squadron's worth of kills. He'd appeared in two scenes before that one, but in those instances he mostly served to take Corran down a peg, be annoyed that half the squadron was politically appointed, and state his absolute, unswerving trust in Tycho Celchu.
The first book in the Enchanted Forest Chronicles starts by establishing a fairy tale kingdom that is perfectly normal, perfectly safe, and perfectly boring. The book that goes on to say that "Cimorene" (the main character) "hated it" establishing her Rebellious Princess role for the rest of the books.
This Immortal by Roger Zelazny: the first scene is of Conrad, the protagonist, slipping up and then having to admit to his new wife that he isn't really twenty-something, and then covering up with yet another lie. This shows us a lot about Conrad, because he's really hundreds of years old and his real name isn't even Conrad.
In The Chronicles of Amber, the hero wakes up in a hospital with no memories and casts on three (unbroken) limbs. He proceeds to Groin Attack the doctor that tries to sedate him, blackmail the hospital manager into giving him cash, and then bluff his sister into believing that he knows everything.
Chronicles of Chaos by John C. Wright: the Red Soldier's introduction is one of these—not so much through what he does (walk down a driveway and enter a meeting), but how he moves and the way it's narrated.
In her first scene, Kate Daniels is drinking alcohol alone in her dark kitchen in the middle of the day, only to whip around and throw a knife into the throat of the vampire sneaking up on her. Her status as a Badass fighter and her hatred of vampires are constant throughout the series, and her loneliness, depression and alcoholism are all Character Development arcs she struggles with.
In the Night Huntress series, Cat's first scene shows her getting pulled over the cops with a vampire's corpse in the back of her truck (and since they're under the Masquerade, the cops won't know a vamp corpse from a human). She keeps her cool throughout, and her politeness never wavers as she says goodbye to the helpful police officer and drives off. Later in the book she proves to be quite calm and businesslike in familiar situations, and quite casual about non-human deaths.
The second scene of Soul Music introduces us to Susan Sto Helit, when her headmistress informs her that her parents have died. The headmistress then prompts her that maybe she'd like to cry or something, and Susan responds "Would that help?" This leads into to another interview with Miss Butts, which establishes her psychic invisibility, and tendency to use this to avoid anything she doesn't want to do. (Which, in turn, tells us that she likes Logic and Maths, but not Language and History, because those are the classes she's visible for.)
Tiffany Aching gets her in The Wee Free Men inside Miss Tick's tent. After being informed that the Queen of Elves is planning to invade the Chalk, Tiffany immediately asks "Can I stop it?", whereas most nine-year-olds would say "Can anyone stop it?" or "Can we stop it?". Miss Tick is very observant of this.
We first meet Lord Vetinari in The Colour of Magic. While talking to Rincewind, he makes it quite clear that not only does he know about the wizzard's attempt to duck out of the guide job Twoflower hired him for, he also makes it clear that if something does happen to Twoflower and the Agatean Empire's armies attack Ankh-Morpork because of said something, he will make sure Rincewind is the first thing their navy ships meet. Though it doesn't demonstrate the levels of excellence he shows in later novels, our first encounter with the Partician shows us he's not a man to cross, but he does care about his city.
Gone with the Wind opens with Scarlett O'Hara flirting with not one, but two beaux at the same time. Naturally, both men are spellbound by her.
Rhett's skepticism when it comes to the South winning the war.
Percy Jackson and the Olympians: The first chapter of 'The Lighting Thief' has Percy recounting how many school's he's been kicked out of and then defending Grover from a bully.
Later on Annabeth who opens with this winning line:
Inner Percy: "She glanced at the minotaur horn in my hands, then back at me. I imagined she was going to say, You killed a minotaur! or Wow, you're so awesome! or something like that"
Annabeth: "You drool when you sleep."
In the Dale Brown novel Air Battle Force, Grzylov is introduced speaking congenially to the aircrew of a Russian bomber whose operation he is sitting in on...one that involves firebombing the shit out of Chechens. It's a Bait the Dog moment, but it also establishes how he cares for his people while also being utterly ruthless to the enemies of the Rodina, notions that are reinforced when his Disproportionate Retribution for losing a base full of bombers is a nuclear sneak attack on the US that wipes out a large part of the American strategic arsenal.
Samson, the most famous character of the Book of Judges, is touted as The Chosen One who will help his people beat the Philistines. His first line of dialogue crushes all expectations.
"I have seen a beautiful Philistine girl in the next village. I will marry her".
The Bible. "In the beginning, God created the Heaven and the Earth." And then God establishes His unending power with a simple sentence, "Let there be light".
No Country for Old Men began with Anton Chigurh violently strangling a cop then killing a man to get to his car.
Duke Alaric Morgan's first appearance in Deryni Rising, when he and Sean Lord Derry ride into Rhemuth for Kelson's coronation, functions this way on several levels:
Morgan glances down at his sombre black clothing in contrast to the colourful trappings of the coronation guests. Morgan prefers to dress this way for much of his early adult life.
Morgan grieves for Kelson's father Brion, and recalls the harrowing events of the past several days. This is appropriate for Deryni, whose powers are partly psychic and partly empathic, and his reverie functions as an Exposition Beam between the author and the reader, akin to those used by Deryni in-universe. We also learn of an ambush which Morgan survived largely uninjured, establishing his martial credentials.
Morgan comes to using breathing and concentration efforts (part of Deryni training to use their powers) and checks on his injured human aide Derry. Morgan is loyal to his own men and doesn't discriminate against ordinary humans, rather treating them according to their merit.
Morgan's ministrations to Derry are rudely interrupted by a whip-wielding giant-sized Connaiti mercenary announcing "His Loftiness" the Supreme of Howicce. Morgan stops Derry from retaliating (noting the giant was accompanied by six more just like him), but cannot resist indulging his sense of humour. When Derry asks, "By all the devils in hell, what is a Supreme of Howicce?" Morgan replies in a penetrating stage whisper, "I'm not certain. I don't think it's as high as a Quintessence or a Penultimate. Probably some minor ambassador with delusions of his own importance." At a glare from the last of giant mercenaries, Morgan puts on an innocent expression, but once the party has proceeded down the street, he discreetly uses his powers to entangle the whip-wielder's whip round his horse's legs, bringing down both man and beast and forcing the Connaiti to cut the whip to rescue his horse. If life for Gwynedd's Deryni is a dangerous game of Grandmother's Footsteps, Morgan is an expert player.
At the castle courtyard, Morgan dismounts and looks over the courtiers for faces he knows, thereby introducing them to the reader and establishing his thorough understanding of politics. After exchanging greetings with a friendly minor lord, he notices people near him reacting to his presence, realizes they know who he is and have heard dreadful rumours about him, and strikes a pose while dusting off his clothes before slowly gazing on the little assembly to play up the menace. Morgan cultivates his dangerous reputation and uses it to protect himself.
Mother Winter gets one in Cold Days when she describes Mab as "a romantic."
Harry: And that tells you pretty much everything you need to know about Mother Winter.
On the first page of The Hunger Games, Katniss establishes herself as a doting older sister who has no problems with drowning pesky kittens.
It is established to be a truly horrible creature that preys on children when it hides underneath a storm drain and then attacks and kills a child by biting his arm off.
The Fire-Us Trilogy open with Teacher (who reads and interprets her "sacred" Great Big Book of Everything), Hunter (who collects resources to feed and supply the family), and Mommy (who takes care of the younger children) all performing their respective duties. Later, Angerman is introduced in the middle of one of his fits.
The first time we see the titular character of Skulduggery Pleasantin the flesh, he kicks down a door, snarks, throws a fireball and fires a gun. Yep, that pretty much sums him up.
Lenobia's introduction in the House of Night series. She rides in elegantly on a horse, bluntly tells her new students that half of them won't last the semester, and warns them not to slack off ("Horses are not big dogs. Nor are they a little girl's dream image of a perfect best friend who will always stand beside you. Horses are work."). But she also allows her students to ask questions, mentions that she chose her name as a historical reference, and has a friendly chat with Zoey after class. Three pages, and we know that Lenobia is confident, stern but fair, and very knowledgeable.