One travel-related commercial featured a family with a seemingly somewhat quieter version of this trope, with the mother marveling at how her daughter was actually smilingfor once because she was having so much fun on vacation.
Louise Halevy starts like this in Gundam 00. When she stops being like that, it's through a heart-wrenching Wham Episode... and she ends up as a Tyke BombDark Action Girl. She finds and goes to town on Nena Trinity who caused it. It takes her and Saji a LOT to get her better.
Invoked by Aya in Nicoichi, who was tired of being Spoiled Sweet by her father and wanted him to treat her more normally. How much of this personality being actually an act is up to anyone's guesses though.
Cher Horowitz from Clueless is a good example of the smarter (if still shallow and naive) version and is also unusual in being the actual protagonist. She's also sweeter and more considerate than the usual example in several ways, in that she's constantly fretting about her father's stress levels and need to have a proper breakfast, and reaches out to make friends with the awkward and unfashionable newcomer to the school (for pretty shallow reasons at the time, but still).
Luke Skywalker in Star Wars comes off as a male version at first, although it's pretty understandable (his foster aunt and uncle forbidding him to pursue his dream of attending the Imperial Academy and becoming a pilot like his father). He does whine and moan quite a bit throughout A New Hope and The Empire Strikes Back, although by Return of the Jedi this behavior has completely disappeared. And through it all, he looks pretty sympathetic compared to Jerk with a Heart of Gold Han Solo.
The teenage daughters of the protagonist in Dan in Real Life, who spend the entire movie whining and sulking about, in one case, not being allowed to drive the car, and in the other, being separated for a few days from the boy who is kind of their boyfriend. While their behaviour is kind of bratty, the girls do have bigger underlying issues and sympathetic reasons that were later revealed Mom's dead, Dad is super overprotective.
Cassie Munro (played by teen pop singer JoJo) in RV.
Sarah Gopnik from A Serious Man qualifies, thanks to her vanity and frequently obnoxious attitudes.
This is deconstructed in the Film NoirMildred Pierce. Fiercely protective mother Mildred tries to do anything to please her daughter Veda, who is an unappreciative brat. Mildred ends up ruining her own life just to try to get love back from her daughter.
Audrey Griswald was very much this in National Lampoon European Vacation. During practically all of this movie, all she does is whine about her missing her boyfriend and her weight.
Sarah from Labyrinth begins the film acting like a complete spoiled brat who blames every problem she has on her stepmother and half brother. The events of the film mature her.
Also a subtle deconstruction. She's a spoiled brat with a roomful of toys and pitches fits, but her parents are emotionally unavailable at best and passive-aggressively snide at worst; her outbursts are obvious cries for attention. The movie ends with Sarah learning to turn inward for comfort, without losing perspective in the real world.
As one of the two main protagonists of Galaxy Of Fear, thirteen-year-old Tash Arranda doesn't display much of this - her family lived on Alderaan and she's had to step up to look after her little brother, plus she's constantly being dragged into danger. With everything going on she has to be focused on surviving, what's left of her family, and, when there's time, The Force. However, there are a few hints of the trope now and then - at the start of Planet Plague things are pretty quiet, and she locks herself into a refresher to study new pimples in the mirror and angst over them, thinking "They were as noticeable as orbital beacons." In The Brain Spiders her efforts to be "adult" cause her little brother to sigh "Teenagers!"
Charlie And The Chocolate Factory: Veruca Salt, and to a lesser extent Violet Beauregarde, are the "examples" of bratty teenage daughters there to teach a lesson by having horrid things happen to them. As with the rest of the children who aren't Charlie.
Live Action TV
Astor from Dexter... just... wow. Although she does have a Freudian Excuse that gets worse as the series goes on. Also Deb in some flashbacks.
Rae from My Mad Fat Diary falls into this stereotype in some of her interactions with her mum.
Subverted by Maeby from Arrested Development. Her parents assume that she's just a moody teenager and make it a point not to question her motives or activities. In reality, she's secretly a high-ranking executive at a movie studio and tends to make out with two of her cousins. Of course, it turns out she's not related to either of them.
Whose Line Is It Anyway?, Colin Mochrie, as a news anchor, once had his teenage daughter (played by that week's female guest) appear on the news, and she was so comically immature that he responded, "Well, that was an experiment that went awry."
Power Rangers Ninja Storm similarly had Marah and Kapri, Lothor's Bratty Teenage Nieces. They're only related by marriage, but it's apparently enough for Cam, Lothor's nephew, to consider them "cousins" and give them a second chance in the season finale.
Dawn Summers from Buffy the Vampire Slayer often borders on this trope, but a lot of it is understandable given what happens to her in season five. She grows out of it the last season. Buffy herself fit this trope on more than a few occasions.
Emily Lightman from Lie to Me is usually an aversion of this trope, but bringing a boy home during school hours and complaining that "It's just sex" when her father figures it out suggests she's moving toward this.
Alexis Castle in Castle is a delightful subversion of this trope, being consistently both one of the most well-adjusted and down-to-earth members of Richard Castle's entire family. She does have her moments, but they're usually triggered by her father's immaturity(-stroke-overprotectiveness) rather than the other way round.
It's at times hinted that Beckett went through one of these stages as a teenage girl; the advice she often gives to Castle whenever he raises an issue he's having with Alexis often seem to come from the perspective of someone who knows first-hand exactly what a Bratty Teenage Daughter can be like. The death of her mother appears to have put a rather brutal end to it, however.
Discussed In the The Legend Of Korra episode "A Leaf in the Wind" when Tenzin expresses frustration with his teenaged live-in Airbending student, Korra (the fact she's the reincarnation of his father Aang provides a very odd family dynamic). After his daughters witness a particularly bad bout where Korra insults Tenzin's teaching skills, Tenzin tries to avoid the inevitable.
Tenzin: You must promise me your teenage years won't be like this!