Nelson and his fellow bullies on The Simpsons certainly qualify here. In the hockey episode, where Bart tries to show up Lisa in school because she's playing well on the ice, he gets every single answer he volunteers wrong. Cut to him being beaten up by Nelson. "Here's for wastin' teacher's valuable time!". In a later episode, Nelson beat Bart up once for "Stealing credit from someone else", along with another bully concerned with church issues because "Not only am I a teenager, but the father of a teenager." Nelson also beat Bart up for "Besmirching a lady's good name". In summary: Nelson will use any excuse to hit someone.
In fact many of the children at Springfield Elementary give Bart and Lisa a hard time when they face a dilemma of embarrassment, most notably Janey Powell and Sherri & Terri. It's even one of the three main "rules" of the Code of the Schoolyard. This trope is then driven Up to Eleven in "Lisa Goes Gaga".
While Bart gets bullied often, he is also far from innocent as he regularly terrorizes his family with his pranks (sometimes with big consequences) and mean spirited remarks and has tormented Homer enough to make him cry at least several times.
Homer recalls an incident from his childhood where another group of kids formed the "No Homers Club" to keep him out. Marge paraphrases this, but unfortunately Bart overhears...
Lisa: (in the other room) Ow ow ow! Stop! MOOOOOMMMMM!!!
Even Ned Flanders wasn't immune to this. His parents were beatniks who didn't believe in discipline, turning him into a rather crazed brat. He was subjected to a radical form of child therapy (basically getting spanked by the doctor for an entire year) to rein in his destructive behavior, turning him into the nice guy we know. Unfortunately, the treatment worked too well, making it impossible for Ned to express any frustration, leading to him bottling up all his anger until it boiled over at the worst possible moment.
An American Tail had a group of mean, cynical orphans near the end who briefly convince Fievel to give up looking for his family.
Ed, Edd n Eddy in particular are known for being disliked and harassed by just about every character on the show, except the Kankers, though they tend to sexually harass the Eds. This is because Eddy scams people out of their money and pressgangs his two friends into helping him. Ed and Edd are shown to be moderately accepted when not being blamed for Eddy's behavior. Hell the Ed's sometimes attack each other when no one else is bothering them. Johnny, Jimmy and the Kanker sisters aren't known for being liked that much either (though the Kanker sisters actually fight back whenever someone messes with them).
Futurama: As a child, Leela was mocked by the other kids for only having one eye. Even the blind kid hated her ("At least I have two of them!"). It seems their favorite pastime was pointing at her and chanting "One eye! One eye!" Whatever torment they dished out on her, however, was probably preferable to what they would've done if they knew she was a sewer mutant and not an alien (aliens are automatically given civil rights, but all mutants are forcibly confined to the sewers, which is why Leela's parents left her at an orphanage with a faked note in alien writing, hoping to give her a better life).
Even as adults they continue to taunt and tease her, despite all growing up to be bums, drunks, and jobless lowlifes they still feel superior to Leela despite her job as a ships captain and laugh at the idea that she should feel sorry for them.
She responds to taunts with violence (having broken the blind kid's nose several times), a trait that has carried over into adulthood, where her response to many situations is to kick/punch someone. It was even a key focus of the third movie.
Except for the main characters? Zim is trying to take over and/or destroy Earth as well tortures and experiments on his classmates, and Dib's not the nicest guy either.
Actually, Dib is the nicest guy on this show. Although he's arrogant and at times selfish, at the end of the day, his intentions are to protect Earth from an Irken invasion and he has more than a few moments where he shows protectiveness of Gaz, not that she needs it.
Subverted in the pilot, where Zim passes off his green flesh as "a skin condition". One of Dib's classmates chews him out for picking on Zim for being different.
Danny Phantom: Danny Fenton was more of a victim of bullying before he got his ghost powers and was able to teach Jerk Jock Dash a lesson. Still, the other kids, namely Dash and his group of friends, never do stop bothering him.
Namely because Dash and his friends never found out about Danny's powers...well, they did twice—one time he acted nicer, and the Reset Button was pressed, the second time was in the final episode, so we don't know for sure if the bullying stopped.
Hell, we don't even know if they EVER found out. There was what, seventy people in that crowd when Danny changed back to human? The rest of the world may not have found out at all. They could have sworn secrecy for all we know.
There is also Sidney Poindexter, a kid who was so ruthlessly bullied in his years at Casper High that as a ghost he haunts the school avenging tormented bullying victims. He ends up targeting Danny because he sees him locking Dash in a locker as revenge and misunderstands the situation.
To the point where it crosses over from Kids Are Cruel to making Timmy the universe's Butt-Monkey. The bully Vicky is more a force of nature than anything and barely has any characterization. This is actually what drives the show, as the reason for why Timmy got his fairies in the first place is because of the misery Vicky put him through.
Most of the kids in Hey Arnold! depending on the episode.
In Blinky Bill, Marcia Mouse can sometimes be downright mean to Shifty Dingo.
The Loud House: It's revealed that six-year-old Lola would sell or destroy her siblings' prized belongings if something even mildly annoying happened to her because of them. It's all Played for Laughs though.
The Powerpuff Girls (2016): In the episode "The Wrinklegruff Gals", the girls are the victims of this by their schoolmates at their K-8 school.
The Lemonade Stand Gang in Dan Vs.. They get theirs in the end though, just like almost every other target of Dan's vengeance.
Though they get sent to military school, instead of reform school like Elise suggested, so they might come back worse than before.
Family Guy has one episode where a pre-teen beats up Chris just to prove that he is Mr. Herbert's paperboy now and Chris can't do anything about it. The boy is joined in by his friends as they all pick on Chris and laugh at him as Chris gets a bloody nose from the fight. Even though the bully is forced to apologize, he reveals to Peter that bullying makes you feel like you have power and that the more you bully people, the better it feels. This causes Peter to become a bully to his neighbors until he realizes he is becoming the same bully that picked on him when he was in school.
Diamond Tiara and Silver Spoon from "Call of the Cutie" tease Apple Bloom mercilessly for being the last filly in her class to earn her "cutie mark".
"Lesson Zero" seems to take an in-universe fear of this to poor Twilight Sparkle, who seems to fear being sent back to Magic Kindergarten because of the possibility of this trope.
"One Bad Apple" has Babs Seed, a cousin of Apple Bloom, who picks on her and the other Cutie Mark Crusaders. It turned out she was doing this to avoid being a target of bullying from Diamond Tiara and Silver Spoon.
In "Cutie Mark Chronicles" and "Hurricane Fluttershy" it's shown that Fluttershy was mocked for being a weak flyer when she was a filly which still affects her as a grown-up.
The lack of television shows and movies acknowledging this was one of the things that led to the creation of South Park.
The Sugar Rush characters in Wreck-It Ralph are meant to be around age ten. They aggressively bully Vanellope, who is referred to as "The Glitch" due to her being a glitch, to the point where they break her car in order to get her out of a race. They were programmed by King Candy to act this way. When they regain their memory they are a lot sweeter to her, though it may partially just be fear as she is royalty and could reprimand them.
In "Nothing to Fear", Scrooge's greatest fear is being told by Huey, Dewey, and Louie that they secretly can't stand him and only want his money.
We created that magic raincloud with our Junior Woodchucks chemistry set...JUST TO RUIN YOUR DAY!
In "Superdoo", even Huey, Dewey and Louie aren't above making snide remarks about Doofus' slowness and weight.
In The Smurfs episode "The Tallest Smurf", Nat, Snappy, and Sassette pick on Slouchy for being the shortest Smurfling. Of course, they end up eating humble pie when Slouchy makes a wish to be the biggest Smurf in the village, and Gourdy fulfills it by making all the other Smurfs bug-size.
In a later season Robot Chicken short, the cast of G.I. Joe realize that they are somehow being mutilated without remembering it, as evident by the fact that people suddenly have the wrong body parts or have been drawn on. At first they assume Cobra Commander is behind it, until they discover he's missing the entire lower half of his body and screaming about a horrific, godlike being that has brought Judgment Day upon them. It then cuts to a live action kid mutilating another action figure with his bicycle wheel. The Joes then shoot him in the back, but then realize they just killed a kid.
While some child characters in Tom and Jerry were often too young to understand what they were doing as wrong (such as Nibbles/Tuffy/whatever-his-name-is and the runaway baby Tom and Jerry sometimes had to rescue), a very straight example would the the three kittens in "Triplet Trouble" who attempt to injure Mammy-Two-Shoes when her back is turned and proceed to torment Tom in rather cruel ways as soon as she leaves, and when Jerry attempts to mess with Tom along with them, the kittens promptly begin to make his life a living you-know-what, too, simply because he was there. Eventually, Tom and Jerry decide they've had enough and teach the three kittens a lesson.
In Whatever Happened to... Robot Jones?, the title character is often ridiculed and mocked by the human children at his school. Even his three closest friends Socks, Cubey, and Mitch can be hurtful at times, like when they tease him over his crush on Shannon Westerburg in "Embarrassment" or taunt him over being unable to grow hair in "Hair".