In "The Boogeyman," the Unsub turns out to be a young boy named Jeffrey, who would lure other kids into the woods and then beat them to death with a baseball bat. The team is able to stop him before he kills another kid. While in the backseat of a cop car with Jeffrey, Gideon asks him why he killed all those kids, and Jeffrey simply responds with "Because I wanted to."
In "A Shade of Gray," the team is trying to solve the murder of a young boy named Kyle, and the culprit turns out to be Kyle's older brother, Danny, who got angry at Kyle for accidentally breaking a model airplane Danny was working on, and he killed Kyle by shoving the plane parts down his throat.
"Safe Haven" introduces us to Jeremy, a 13-year-old psychopath who went on a cross-country killing spree by convincing families to allow him into their homes where he would kill them. Later on in the episode, Jeremy's mother is seen talking to someone on the phone about all the awful things Jeremy has done in the past, including putting rat poison into the Thanksgiving turkey, killing his neighbor's dog, and breaking his little sister's arm.
In the CSI: Crime Scene Investigation episode "Cats in the Cradle," the team is trying to solve the murder of an elderly woman who lived with at least a dozen cats. The murderer turns out to be an eight-year-old girl who lived just across the street from the woman. Her motive? She wanted to adopt one of the woman's cats, but the woman refused, making the girl angry. She then grabbed the cat she wanted, handed it to her sister, and told her to run home with it. She then shoved the old woman to the ground and stabbed her in the heart with a pen. She also forced her sister to keep the murder a secret by telling her that "Tattletales burn in hell."
Doctor Who: In "Fear Her", Rose argues for this trope as she and the Doctor are discussing his sympathy for Chloe and the alien possessing her. The alien itself draws an image of Chloe's abusive father to protect her... though it's heavily implied that Chloe willingly drew the image along the alien to keep her protected.
Drake & Josh: Megan is the textbook example of this trope, constantly tormenting her two brothers for kicks. It occasionally reaches Enfant Terrible levels, such as in "Vicious Tiberius" and "Helicopter"; the former has her knowingly leaving the two with an aggressive dog, and the latter has her ignoring their serious call for help over stickers. Of course, she is often a Karma Houdini, mostly due to playing saint next to her parents and using Wounded Gazelle Gambits to make it seem like the two are tormenting her.
Simon on FlashForward (2009) was bullied as a child growing up in Canada because of his accent and for being a Teen Genius. Until one day, when he filled his lunchbox with rocks and beat the crap out of the bullies with it.
The Law & Order episode "Killerz" involves a ten year old girl who casually murders a six year old boy for the fun of it, and receives a slap on the wrist for it. During her psychological evaluation, she casually admits to poisoning the neighbors pets, of enjoying having killed someone, and of having plans to kill again.
Dr. Emile Skoda: She's a Serial Killer. We just caught her early.
What's equally sad is the likelihood that the girl is a sociopath because of abuse she herself suffered — her father's in jail and she has tolerate her promiscuous mother bringing numerous lovers home and not even bothering to close her bedroom door when she has sex with them — it is implied that any number of these men has made advances to her as well. Is it any wonder that she's completely screwed up with a hatred of all things male?
Law & Order: Special Victims Unit had an example of a very young-looking thirteen-year-old date-rapist who was pushing his victim to get an abortion; his secret lovechild half-brother who had a crush on the victim killed him when it seemed like he was going to take matters into his own hands. There's also the two fourteen-year-old girls who almost succeed in pinning the murder of an eight-year-old on a developmentally disabled neighbor — actually one girl was "normal" and the other was the psycho/sociopath who tortured the kid because it was funny and strangled him because he was gonna tell.
On Lincoln Heights, when Lizzie gets a basketball scholarship to an upper class boarding school the students initially appear to be welcoming, but it later turns out that they are racist, manipulative elitists who couldn't care less about her as a person and only care about her basketball skills. Basically, they expect her to act like "a girl from the hood." And the adults aren't much better.
Midsomer Murders likes this one; at least three episodes have children as murderers.
In the New Amsterdam (2018) episode "The Karman Line," Iggy must deal with a young sociopathic girl who tried to strangle her little brother to death all because he wouldn't let her play with his phone. In one scene, Iggy tries an experiment where he will give the girl some play money everytime she apologizes for something, but the girl just thinks that this means she can do whatever she wants and get away with it as long as she says "sorry," so she starts doing mean things to Iggy, like calling him names, saying that he's fat, and even spitting right in his face. Towards the end of the episode, the girl does apologize to her brother and promises her parents that she will try to control her anger, but then she walks up to Iggy and reveals that what she just said was all an act.
An episode of The Office had a gang of kids attack Pam and Andy, later when confronted and asked why they assaulted them and threw things at them the leader replies because Pam was fat and they thought Andy was gay.
The main character of Pushing Daisies was picked on at Boarding School, because of his introversion and his tendency not to retaliate. And when he did retaliate, the bullies waited until he was alone and then beat him up.
The Twilight Zone (1959) episode "It's a Good Life" features the cruel, sadistic, and omnipotent Anthony Freemont, age six. The episode basically shows what would happen if all of the selfish whims of a child were able to be fulfilled due to the child happening to have been born with incredibly strong, telekinetic powers. Anyone who tries to defy him gets killed, or worse sent to some place Anthony refers to as "the cornfield" where they're trapped for all eternity.
Kenard in The Wire. What sets him apart is he truly is a sociopath. In one episode he douses a cat in lighter fuel in one scene and kills someone in another.