Many 90's kid-aimed commercials glorified this trope, with kids joyfully behaving in ways that even most real-life kids would find repulsive.
A good example is the Kellogg's Frosted Mini Wheats commercials of the mid-90's, which not only exemplified Kids Versus Adults but often had cartoonishly sassy children doing things almost no decently raised kid would even want to do in real life, such as squirting (reasonably nice) old ladies with garden hoses.
Kids in cereal commercials are especially cruel to mascots, with the most notorious examples being Lucky and the Trix Rabbit, who will never get to keep or have their respective cereals thanks to them.
The beginning of the Star Trek fic Safe and Sound has the young Lucille Harewood confronted by two boys who accuse her of being a terrorist like her father - and proceed to beat her up for it. If she hadn't had Khan's blood in her, she would've been seriously injured.
From the Gensokyo 20 XX series, we have Yume Ni "Yu" Yakumo and it is to such a degree that the other kids prefer Reimu over her, especially, when she hits them. Apparently, she seems to have a Lack of Empathy, seeing as she tried to throw Reimu (attached to an IV) over a railing, the which of could have either killed or injured her, along with a nonchalant to eager tone about the other kids being her bitch.
In Redrum 327 Hyeri. At mere eight years old, Hyeri and the other kids locked Gahui up in an abandoned safe in the middle of a forest, where Gahui ended up being trapped for six days while it rained, nearly drowning and half frozen as a result.
Check out Girlfriend by Avril Lavigne for an example where the bully is the protagonist.
Rory: Ha ha ha ha... er... Ahem hem, er, kids can be so cruel.
Adventures in Odyssey: Liz Horton was a rather nice girl, but you wouldn't know this from her first appearances. In two episodes, the first she repeatedly teases a girl about how ugly her clothes are, ((even informing her that she was talking about her)), and in the other episode she is so mean at times, you just want to reach through the speakers and punch the ever living tar out of her.
Donald Glover discusses this in one of his stand-up routines, describing children as "tiny Hitlers". He says that walked by two kids fighting over a basketball, and the fight ended with one of them saying, "And that's why your mom's in a fucking wheelchair!". Donald was so shocked he dropped the food he was carrying, and wonders how someone can say that without exploding.
Kid World, from the somewhat obscure company of Vajra Enterprises, is a post-apocalypticLord of the Flies on a global scale after a plague kills ninety percent of humanity and leaves all the adults blind. Earth is a giant shithole.
Tedd of El Goonish Shive has been made fun of since he was small for being androgynous; his AU counterpart went nuts from the strain. Justin has been teased since early high school for being gay. Susan has always been considered a weird feminist, but she got really reamed for a few days after showing up at school in the boys' uniform.
In Gunnerkrigg Court, it seems that prior to Antimony's arrival, the entire Queslett North class made a point of ostracizing Kat Donlan, simply because she got good grades and had teachers for parents.
Part of this newfound respect for Kat may be simple fear of Annie. Its shown that despite the class having respect for her, they're kind of freaked out by her Emotionless Girl status at the same time. Ironically, this makes Kat the sociable one and Annie the quiet one, as the class tend to ask Kat to pass messages along to Annie. Kat, naturally, calls them on this.
In Girl Genius, the children aboard Castle Wulfenbach are noted by Tarvek in this comic as tormenting and picking on each other all the time. Lineage, as he comments, was a favored excuse, with them taking any chance to "one up" each other and thusly claim a reason to bully their "lessers" around.
This might be Unreliable Narrator, as Tarvek is not unbiased on the subject. Though they're old enough to mostly not be "kids" any more, only one of the Castle students (Princess Zulenna) goes out of her way to be cruel to Agatha when she's living with them, despite everyone at the time thinking Agatha is a commoner nobody.
In the lonelygirl15 episode "Poor Pluto", it is revealed that Bree was bullied by the other kids at school because she liked to ask questions about stars. However, in the following episode, "I Want to Take Bree to a Party", Daniel claims that it was just teasing and that Bree takes things really seriously they were a bunch of mindless jerks who didn't give a crap about her feelings. Seriously, spreading rumors about her having an affair with her teacher?