Adult-on-child violence is rare ... except for instances where Homer chokes Bart (usually when Bart says something he shouldn't and it gets Homer in trouble). The strangulation issue with Homer is the most common instance of this trope, but Bart Simpson in general seems to have this effect on many adults in the show.
The villains aren't exactly above hurting children, especially Bart. Sideshow Bob has repeatedly attempted to kill Bart. Fat Tony has on several occasions had his crooks threaten Bart with violence up to and including murder. Burns threatens Bart with a gun prior to attempting to drown him as seen on the page picture, and that's apart from repeatedly letting The Hounds loose on him. Snake Jailbird has tried to run over Bart with his car, but as always, Bart's Plot Armor makes sure that the alley he is standing in is too narrow for Snake's car to pass.
From "The Great Wife Hope" there's Chet Englebrit, commissioner of the "Ultimate Fighting League." During a fight with Marge, Bart comes up to him to challenge him. His response is, "Heck, I'll fight anyone. Except a man my own size". Seeing Bart about to get hurt is what puts Marge on the edge.
Family Guy: The flanderized Peter Griffin from the later seasons frequently attacks and occasionally murders people, and children are no exception. He punched out a child because he felt he had to hit someone, blew up a children's hospital (although that was an accident, but still), killed his own infant son Peter Jr. when he couldn't get him to stop crying, and threw his toddler son Stewie (who was in a coma with heavily infected wounds) under his wife's car so it would look like an accident. Let's not even get started on what he does to Meg.
Another memorable segment saw Peter use Lucy Van Pelt (from the "Peanuts'' comic strips) as a punching bag after he grew tired of her picking on Charlie Brown.
Soundwave and Blackarachnia in Transformers Animated have threatened Sari. The former even tried to make her own father murder her.
There's also Meltdown, who once kidnapped Sari with the intent to do unethical experiments on her.
South Park episode "Stanley's Cup" plays this trope straight.
From "Terrance & Phillip: Behind the Blow", the Earth Day Brainwashing Committee (who might be the episode's antagonists) aren't above chopping off Kenny's limbs.
The infamous ending to "Jared Has Aides" has Butters getting brutally beaten by his parents after Cartman tricks them.
"The Death Camp of Tolerance" has the Tolerance Camp Warden, one of the most cruel and sadistic characters Trey and Matt have ever come up with (besides Cartman), routinely threatens to kill the kids if they don't meet up to his expectations, especially poor Kyle (because the episode in question is based off of Schindler's List and Kyle is Jewish.)
The robbers from "Super Fun Time". They even threatened to kill Kenny and were seconds away from pulling the trigger when Stan intervened.
Hell, with the type of show South Park is in general, there are many, MANY people who are willing to hurt, or even kill, children.
He's also made a few attempts to murder him. He was talked out of it the first time by his wife and the second time Zuko barely blocked his attempt in time and ran for it.
TheBoulder once felt conflicted about attacking a young, blind girl. The Boulder soon overcame his conflicted feelings and tried to bury her in a Rockalanche! The Boulder got completely trashed in the ensuing fight. Then again, this section is a parody of the WWF and The Boulder seems to know Toph well enough later in the show, it's quite possible all of this was just a play for the audience.
Katara's mom Kya knew that Fire Nation soldiers would harm and capture whoever the last waterbender in their tribe was, regardless of age, which is why she gave herself in, and not her daughter. 'Harm' in this case actually meant 'kill'.
This definitely be applied to Sozin. He ordered the deaths of Airbending children. Who were raised to be pacifists. All of them.
Koh the Face-Stealer was quite delighted to see Aang. It had been some time since he had taken the face of a child.
The Kangaroo Court in "Avatar Day" had no qualms about boiling Aang, a twelve year old boy, in oil.
In the sequel, Tenzin's three kids are under 10, but this doesn't mean they're spared of being attacked or being this close to being de-bended by the Equalists. Since they're Airbenders like their dad, they do their best to fight back.
In Season 2, Korra's Uncle Unalaqups it to eleven and threatens to destroy Jinora's soul if Korra doesn't open the northern spirit portal for him. Despite Korra's compliance, he sends Jinora to the Avatar's version of Hell, making Unalaq one of the worst examples of this trope in a children's show.
In Season 3, the Dai Li show up again, unlike the average earth kingdom guards, who find Jinora and just scold her, they're willing to engage children with a lot more force the air benders forcibly conscripted, are frequently hit with earth discs to train them, and Kai is taken down with a barrage of them when he gets uppity.
And now, we have the Red Lotus threatening to kill everyone at the Northern Air Temple. In fact, P'Li actually shoots Kai out of the air, leaving it briefly ambiguous as to whether or not the latter even survives. (He does.)
Futurama: "Parents, have you ever just tried turning the TV off, sitting down with your kids, and hitting them?"
In ThunderCats (1985), villains rarely care that Wilykit and Wilykat are children, often taking advantage of that fact to use them as hostages. This becomes especially bad in some episodes like the one with Safari Joe; the Thundrainium he used to restrain the team was hurting them far worse than it was the adults, as Cheetarah pointed out. (Of course, bad guys in the series can be rather cruel bullies, kidnapping, enslaving, and tormenting the peaceful races of Third Earth on a regular basis.)
Queen Bee has no hesitation in placing the young boy Garfield under her thrall. If she wants, she can easily make him hurt himself. Even creepier, she acts affectionately (in a somewhat twisted manner) toward him while stating her threat.
Count Vertigo was willing to let his own niece, Queen Perdita, who needed a heart transplant, die on the operating table because it would make him the King of Vlatava. Unfortunately for him, Kid Flash reveals the young queen with a recording of the Count's Engineered Public Confession, as he thought he succeeded. It's enough to strip him of his "diplomatic immunity" for treason, and Kid Flash tells the security guards, "Take him to Belle Reve." There the Count is laughed at by the inmates for his failing.
In Thundercats 2011, Mumm-Ra and his army considers all surviving cats a threat, including kittens WilyKat and WilyKit. The task force consisting of Slithe, Kaynar, Sauro, and Kask is especially nasty in this regard.
In the episode "Children of the Force", Darth Sidious is perfectly fine with performing potentially lethal experiments on infants. Cad Bane, who kidnapped the infants for Sidious, didn't really care what happened to them, so long as he was paid.
In "The Academy" Prime Minister Almec threatens to kill Satine's nephew if she doesn't give in to his demands.
In "Revenge", Darth Maul butchered dozens of innocent people, including several young children, to attract Obi-Wan's attention.
In Death Trap, Aurra Sing displays no compunctions about the idea of abandoning an escape pod full of clone children to die in space - saving only Boba - because the kids are witnesses to their crime. She even seems faintly amused by it.
Megatron from Transformers Prime. When he found out that he near-fatally poisoned Raf with Dark Energon while shooting at Bumblebee, he was downright pleased.
Megatron: Well, well. It looks as though I swatted a bee, and squashed a bug.
The Earl of Lemongrab from Adventure Time goes COMPLETELY BATSHIT CRAZY in the episode "You Made Me!", and ends up electrocuting three young children and a 14-year-old boy, and assaulting a baby. His more malicious side was hinted at in an unused storyboard for "Too Young," in which he screams at a candy child and sends him to the dungeon for no reason, making the kid cry. This aspect of his character was not confirmed until "You Made Me!".
The Flame King ordered one of his minions to turf out Flame Princess when she was a baby and leave her to die. Fortunately the minion couldn't go through with it.
In "The Underdwellers". The Sewer King is exploiting and abusing children. Batman finds out and is less than thrilled. For just a minute, the viewer wonders about that train...
The New Batman Adventures has the new Robin meeting Two Face -who says he'll happily twist his neck.
The Joker subverts this at first in the episode "Be A Clown", where he doesn't seem to care one way or the other if a party full of children gets blown up at the end of the first act; but in the Return of the Joker movie he brainwashes Robin through horrific psychological and physical torture.
In one episode of The Batman, the Penguin acquires two statues capable of focusing light into a death ray capable of destroying buildings; when Batman finds him, he threatens to use it on Gotham Children's Hospital.
One episode has Joker masquerading as Batman, the catch being that the "crimes" he stops are incredibly minor and he stops them by poisoning them with Joker Gas. One such scenario has him attempting to poison two elementary school-aged girls for drawing on the sidewalk.
A later episode has Joker recruiting a Kid Sidekick, and then attempting to throw him in a vat of acid.
Subverted in an episode of Duck Dodgers. Martian Commander X-2 threatens grievous harm to a baby, but the instant said baby begins crying, he reassures the child that it is merely an empty threat and that he would never carry it out.
Although his exact age is never given, Mighty Max is obviously a preteen boy. Not only are his enemies not afraid to attack him, most of them specifically want to kill him in the most horrible way they can think of, and they're not afraid to say so.
Don Karnage in the pilot of TaleSpin. The worst part; Kit's reaction when Karnage crumbles his board before having his pirates throw the kid off the plane indicates he thought that even Karnage wouldn't go that far...and it happening anyway terrifies him.
The Fairly OddParents!: Denzel Crocker in particular. There are several examples, but the best one is at the climax of "Abra-Castastrophe" when he was going to destroy Timmy Turner (Waste in Timmy's words) after the boy surrendered to him.
Many of the various oddities in Gravity Falls don't seem to have a problem with harming or possibly killing Mabel and Dipper. Bill Cipher especially goes out of his way to try and kill or harm the two if the need arises (or he feels like being a dick), and vaporized Time Baby when the latter tried to stop his Take Over the World scheme.
Not only does Ming never exclude Kshin from his various attempts to kill the Defenders (except by default if Kshin is absent from the scene in question) he directly targets the boy on more than one occasion.
In the final instalment of the "Book of Enigmas" arc, Kronos is prepared to reduce Kshin to ashes in order to get his hands on the Book.
Invader Zim: Zim and Dib may be the same height, but Zim is an adult Irken who underwent years of military training before coming to Earth. Dib, on the other hand, is in elementary school. Even though he's a science prodigy with access to his father's equipment, he is by no means Zim's equal — but this doesn't stop Zim from trying to destroy him. Tak's ship spells out the differences between the two in the second issue of the comic:
Takís Ship: Youíre going after Zim. An Irken Invader with untold decades of military training and a history of violence and mayhem. You donít know where heís going or what he plans to do. And you are a feeble, unarmed human in a stolen ship that you have no idea how to use. When you catch Zim. You are going to... what exactly?
Dib: Well... stop him.
Takís Ship: Right then. Tracking Zimís garbage signature for the earthbaby with no plan.