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 however is especially 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.
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 Ed is a comic book geek, Edd is a nerd and Eddy scams people out of their money. Hell the Ed's sometimes attack each other when no one else is bothering them. Jonny, 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).
Can you blame the kids for not particularly liking Johnny? There's an entire episode devoted to him being a pest (and the Eds capitalizing on that).
And on that note, although Edd doesn't deserve the bullying he gets, Eddy usually deserves at least some of it. Ed sometimes does if he decides to ignore Double D and go along with whatever Eddy does, as not only does he try to scam everyone, but he's a self-centered jerkass, which makes Kevin seem somewhat sympathetic by comparison.
I don't think it's as black-and-white as that. With Kevin, he does get provoked by the Eds sometimes, but other times he's a straight-up Jerkass to them, and he and Eddy are actually somewhat arch-rivals in the show. Consider the episode "Your Ed Here", where Kevin finds Eddy's wallet and learns that his middle name is Skipper. He makes Eddy do embarrassing stuff so he wouldn't reveal Eddy's middle name to everyone. After making him do things like dress up like Jimmy, kiss Edd in front of Nazz, and act like a performing seal in front of everyone, Kevin still tells everyone Eddy's middle name. Who is the more sympathetic one mostly depends on the writer. Eddy is a self-centered con-artist, but I wouldn't go so far as to say he's THAT bad.
Really, it's not focused on the Eds. The kids are just violent in general. Pretty much everyone, from the local Brainless Beauty to the girly boy, has beaten up/caused some serious harm to another kid.
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.
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.
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.
In Blinky Bill, Marcia Mouse can sometimes be downright mean to Shifty Dingo.
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.
Meg suffers this in the hands of Connie.
My Little Pony: Friendship Is Magic doesn't shy away from this. 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.