Lymle in Star Ocean: The Last Hope. The voice actress might be the real culprit on this one, not the script/characterization ... it's hard to tell. She talks slow because she's catatonic, but is otherwise played up as a Tsundere, so it's more the latter.
Genis in Tales of Symphonia was bratty at times, but was actually smarter than the main character...and pretty much every character in the game for that matter. And he knew it. Of course, this didn't stop Raine from slapping Genis upside the head whenever he got too carried away.
Luc in the first three games is this. He makes it clear he has no interest in participating in your righteous war, is only voluntarily helpful when he has a personal vendetta and otherwise spends most of his time baiting the rest of your party. He also happens to be the strongest magician you recruit. Even as he gets older through the games, thanks to his immaturity and immortality remains in this trope.
Ted in Suikoden IV is also this. Notable in that he shares the same Star of Destiny slot as Luc.
Mission Vao in Knights of the Old Republic. Subverted when Zaalbar, her Wookiee companion, is the one who ends up getting kidnapped and in need of rescuing.
Soren. Normally, his mouthiness is restricted to disapproving arguments. However, there is one notable scene where he nearly gets himself killed by hurling derogatory terms at a man who can turn into a frickin' tiger. This is subverted later after we learn on his past and his hatred of sub-hum...sorry laguz.
Empress Sanaki is shown to be a bratty half pint who uses her power to make cruel jokes. However, she also helps the heroes quite a bit.
Roan in Grandia II is a subversion. He's introduced as being a whiny brat who demands that the party go get his mommy's pendant, but when he decides to go do it himself and you run after him to rescue him, it turns out he doesn't need rescuing, though could still use more capable fighters' assistance. After he joins the party he's shown to actually be shockingly mature and Wise Beyond His Years. And to top it off, he turns out to be a prince, and subsequently a good king.And even the pendant was of vital importance
The Scout from Team Fortress 2 is the youngest out of the 9 mercenaries — he seems to be a teenager, but is actually about 23 years old according to the Track Terrorizer's description. He has a big mouth and an ego to match.
Baby Amelia Earhart (no, really) in Sam & Max: Freelance Police: The Tomb of Sammun-Mak. Several puzzles involve getting her to do what Sameth and Maximus want, which she never, ever does of her own volition. And when the Devil's Toybox gets stolen from various characters by various characters, she's the one who winds up with it in the end.
She gets better when she grows up; Sameth and Maximus' great-grandsons Sam and Max meet baby Amelia Earheart on Easter Island, but this time she's "baby" Amelia Earheart because she's been drinking out of the fountain of youth. She's not as active in the plot, but she's not such a bitch this time.
Date Masamune's characterization in Samurai Warriors (when he isn't being a Smug Snake), especially in the first game, where even his character model is hilariously tiny compared to everyone else's, including Genki Girl Oichi.
Laura from Silent Hill 2 is an infamous example, but it's not particularly unjustified after you find out about James' treatment of Mary.
A fair amount of the children in The Elder Scrolls V: Skyrim are incredibly obnoxious. Even worse are Jarl Balgruuf's kids, who are quick to belittle and mock you.
The apparently biggest bully in Whiterun is Braith, who happens to be a girl taking money from Lars Battleborn and making boasting taunts to the Dragonborn.
If you adopt a daughter with the Hearthfire DLC and have her live in Whiterun, she will complain about Braith's bullying (your son will make fun of Lars for not standing up to Braith).
Ram and Rom are this to their older sister Blanc in the Neptunia series, constantly causing her trouble. Ram is worse compared to her twin though, because she antagonizes Blanc and Nepgear, even after joining the latter's team.
Jr. Troopa is very annoying. He initially seems like a temporary roadblock in the first part of the game, but he quickly proves himself to be more of a nuisance than a threat. He reappears multiple times throughout the game to try getting his revenge against Mario. Still, even if you find this guy to be a pain, he does give you a great amount of experience.