The show could practically be titled Taunting the Reaper. The entire premise requires that the Grim Reaper never snap under constant torment and do away with the kids.
X-Men: With the powers that crop up, this tends to happen a lot. The writers of the original cartoon seemed aware of this, and supplied a harmless but visible mutant - a timid little man with fur, Neanderthal features, and claws instead of fingernails - as a recurring background character constantly harassed by mobs.
Several episodes deal with people (usually Sid and Stinky), teasing either Harold or Big Patty, either of which can and will beat the crap out of them in retaliation.
"Stoop Kid" has the episode's titular character finally growing the toughness to leave his stoop. Harold, who was not aware of this event, casually mocks the Stoop Kid for staying on his stoop...which promptly leads to the Stoop Kid jumping off of his stoop. Harold freaks out and gets chased by the Stoop Kid.
Stoop Kid: "COME HERE, FAT BOY! I'M GONNA ROLL YOU DOWNTOWN!"
X-Men: Evolution was probably one of the worst offenders, with one bully named Duncan trying to threaten Cannonball. Yeah, threaten the guy who you just saw blow a hole in a brick wall by accident, there's a life-lengthening move. He doesn't even have the brains to back down when the magma-creating girl threatens to burn a hole through his car. This isn't even the half of it. The X-Men team in Evolution had a mostly offense-oriented team, with about half of them having some variation on "shoot deadly stuff from hands" as a main power. Of particular note, people kept on bullying Scott, despite the fact that every time they did there was a good chance he'd accidentally blow a hole in the wall (or them).
This is actually a rare example where it actually makes some sense. Duncan and the others, as dumb as they are, realize that Scott and the others at Xavier's institute were taught only to use their powers to save lives, and that it's not okay to blow up someone for picking on you. Notice how Duncan and the others rarely pick on the Brotherhood mutants. They know that the Brotherhood members wouldn't hesitate to beat the hell out of them for any reason.
To complement the last point, there's also another little gem to show off Duncan's incredible intelligence. After Jean dumps him because he's a jackass he tries to get Scott expelled for using his powers... by stealing his glasses and trying to beat him up with two other friends! Eye beams! Deadly! It's like they want to die. Scott then takes them all down in about a second, with his eyes still closed. They still think that they can take him, only finally leaving when two more X-Men show up.
The X-Men franchise as a whole is basically An Aesop for persecution, oppression, etc. Pick something that can make someone different: race, gender, sexual orientation, etc., you name it, that's what The X-Men is about. Of course, it also happens to be literally about people with superpowers, which can make it into a Fantastic Aesop in the hands of poor writers: yeah, it's wrong to be mean to people who are different than you, but the fact that they can shoot laser beams from their eyes shouldn't be your main prejudice deterrent.
In an odd, "friendly" case, the episode, "The Beast Within". Specifically, Robin's um, "questioning" of a possibly unstable Beast Boy, and with predictably disastrous results.
In the episode "Troq", Val Yor openly belittles Starfire to her face with a racial epithet directed toward Tamaranians, despite her species' Super Strength, durability, Flight, ability to withstand vacuum, energy attacks with occasional Eye Beams, and advanced technology being common knowledge. And apparently multiple aliens have this attitude toward Tamaranians. To be fair, however, while us lowly humans would no doubt be threatened by such a line up, Val Yor has powers nearly equal to hers (minus space breathing and somewhat weaker energy projection), so, from his perspective, the dragon isn't all that tough (though this does make you wonder why he treats the puny, primitive earthlings with respect while the alien princess from an advanced, superpowered society gets treated worse than dirt). Val Yor is apparently motivated by the Tamaranians' trait of allowing emotions guide their lives. Of course, by the end, Starfire not only saves his life, but the team kicks him off the PLANET. Even then, he has learned nothing, concluding that humans were 'just like them'.
Cyborg pretty much put it best when Starfire told him what "troq" meant. If Starfire had lashed out at him she would have proved he was right in his view of her species, something she wouldn't do because he wouldn't give him that satisfaction. (And if you want to look very deep into the episode, Cyborg, being a member of a minority himself, could probably understand.)
In Ed, Edd n Eddy: Ed is unbelievably strong. We're talking strong enough to casually lift a house and drop it on someone's head. Yet he allows himself to get bullied by almost everyone. Sadly, he's just too stupid to realize he could probably kick Kevin's ass. In the movie he does kick the ass of Eddy's much feared older brother though.
...As seen in the episode where he was in a bad mood. He inspired genuine fear in his little sister Sarah, he brought his strength to bear against the same people who usually have no trouble antagonizing him, and in lieu of drumming his fingers impatiently against the tree stump he was sitting on, he dug tracks into it with his fingernails. Hell, even the skies darkened over him. It didn't help that Eddy thinks that Ed was in a bad mood for no reason at all and badgered him to get over it and be happy again. Good thing he went back to his usual, goofy, lovable self by the end of the episode(he was in a bad mood because he had a pebble in his shoe).
An episode of The Venture Bros. combines this with Mugging the Monster. A random bar owner constantly insults Brock's hairdo, and while he likely did not know that Brock is a secret agent who normally murders people who show him disrespect and has a license to kill (which he likes to use with gusto but had expired at that point), Brock was still twice the man's size (in muscle) and had biceps bigger than the man's head. Combined with his perpetual angry scowl, you'd think he'd know better than to insult the guy who looks like he could bench press an armoured vehicle and is looking for any excuse to blow off steam. And of course the first thing Brock does after his License to Kill is renewed? Show it to the guy, who insulted him again on the way in. The next time we see the bartender, he's sporting a fancy new eyepatch.
Parodied in one of Ranier Wolfcastle's films which involves him going undercover as a nerd at a high school. Ranier Wolfcastle is a huge, muscle bound actor, but he's dressed as a nerd so obviously some bullies try to pick on him. They even lampshade it by saying "Look, a huge, muscle bound nerd! That just means there's more of you to pick on." It ends with Wolfcastle throwing one of the bullies through the chest of the other.
Another hilarious example, from the trip to Australia where Bart is to apologize for his prank calls. Homer notices the guard at the gate and mistakes him for a British royal guard, making funny faces at him for a few seconds until the guard punches him hard in the face. "US MARINE, SIR!" Later he starts jumping back and forth across the USA-Australia line in front of the embassy:
Homer: Look at me, I'm in Australia! Now I'm in America! *hops back and forth* Australia! America! Australia! America! * Marine punches him hard as he lands on the US side* Marine: Here in America we don't take that kind of crap, sir!
Yet another episode has an unwilling version by Nelson. After Lisa learns that nerd sweat causes bullies to beat them up, she swabs some on Drederick Tatum. Nelson is thus compelled to bully Tatum, all while begging him not to retaliate.
Drederick Tatum: [rolling up sleeves] I'm afraid you've left me little recourse.
Homer tries this on God Himself when he is raptured but his family isn't. When God refuses to send Homer back for them, Homer delivers this warning to the Almighty's face:
Bonnie Rockwaller's constant petty harassment of Kim- despite knowing full well that if Kim decided she'd had enough, her only choices would be "run" or "catch a beating." A cut scene in So the Drama have Monique and Kim discuss this, where Kim decides that beating on Bonnie would make her a bad student, in comparison to, say, trying to kill Shego at the end of the film.
And A Sitch in Time has Drakken, Monkey Fist, and Killigan go back in time to bully a preteen Kim. When they start on Ron the kindergarten Kim trounces them. Later, Drakken wants another crack at it.
One of the dumbest examples, from "Graduation": Ron, who has just become the Mystical Monkey Master, throws Warhok across the landscape and manifests enough power to bring down a bunch of tripods, making the idiocy of messing with him clear. Warhok and Warmonga still try to attack him.
In My Life as a Teenage Robot, the Kruft cousins take every opportunity to torment and belittle XJ-9 socially, attempting to guarantee that Jenny never, ever becomes anything close to popular. XJ-9, a.k.a. Jenny, is a cheerful, sweet-natured girl who also happens to be a walking, talking, sapient weapons system capable of destroying entire alien battle fleets single-handed. In one episode, with the aid of a more aggressive friend, Jenny finally shows them exactly what she can do to make their lives miserable. Even after she drives them into a breakdown, they don't learn from the experience.
Tex Avery's "A Day at the Zoo" from 1939 has a recurring gag with Egghead (Elmer Fudd's prototype) teasing a lion despite constant scolding from the narrator who warns him that this will end bad for him. The short ends with the lion sleeping peacefully, leading the narrator to conclude that the boy finally went home, but it turns out that the lion actually ate him alive.
In the first episode, Nelson taunts Terry for not being athletic enough (the classic "loser"). When a gang of Jokerz shows up and Terry turns out to have sufficient fighting skills to chase off the entire gang, Nelson's response is "I always knew you were a freak." Fortunately for Nelson, Terry (pretty much perpetually) has bigger fish to fry. Nelson does have some brains, though, because when Terry stands up to him later in defense of helpless nerd Willie Watt, Nelson knows better than to pick that fight.
Nelson: (pushes Willy out of the way) He's not worth it. But you are...some day. (gets in his car and drives off)
Speaking of which, in a later episode, the former typical nerd Willie has just broken out of Juvenile Hall using his newfound telekinetic powers and goes after everyone at school who made fun of him, including Nelson and his cheerleader girlfriend. Even after seeing what Willie can do, and the fact that Willie is no longer a wimp, having extensively used the gym while he was locked up, he still taunts the guy. Willie even agrees to a one-on-one fight without telekinesis, but goes back on his word once Nelson starts winning.
This happens to Lucius on Jimmy Two-Shoes. As a child, he was bullied by his teacher, despite knowing full well that he was the future ruler of Miseryville and that he'd have the resources to fight back one day. Even nowadays the weavils and the Rodeo Clowns love to pick fights with him despite having an entire army at his beck and call. Even Heloise is guilty of this at times.
This happens with an actual dragon in My Little Pony: Friendship Is Magic. In the episode "Dragonshy" a napping dragon is causing problems for everypony by blowing smoke into the town with its snoring. Rainbow Dash's oh so brilliant strategy to make the dragon leave is to yell at it to get lost, then kick it in the face. It takes her less than a second to realize that this was a really bad idea.
Cartman gets his humancentiPad taken away and he starts cursing God. Cue Cartman getting struck by lightning and him sobbing in the hospital.
Another example comes after Stan and Kyle have watched Cartman take some rather extreme revenge. They decide it would be a good idea if they never pissed Eric Cartman off again. Cartman is not superpowered though, just sociopathic.
A literal example occurs in the Gumby episode "The Elephant and the Dragon". Both creatures work for a storybook king (the Elephant as manual labor, the Dragon as a castle guard), but the Elephant keeps picking arguments with the Dragon. This pisses off the Dragon, who torches people's houses with his breath. To stop their arguing, Gumby uses a back-hoe to do the Elephant's job just as efficiently and without arguing with the Dragon (and without torched houses). The Elephant takes the hint and apologizes for causing so much trouble.
As for what they were fighting about, the Elephant keeps asserting that dragons are mythological, and therefore shouldn't exist. The Dragon torches houses to prove that he's real.
In an episode that has Gumby, Goo, and Prickle in The Big City, a mugger (with an attack dog) tries to rob the trio in an elevator after Gumby buys a new guitar. Prickle stands up to the thief and threatens to incinerate his pooch if the mugger doesn't call it off. The mugger doesn't. Cue Prickle breathing a huge plume of fire. The murderous mutt is reduced to a whimpering puppy, and the mugger runs away after the elevator reaches the ground floor!
Sadlygrove from Wakfu has a bad habit of doing this. The worst example of this was when he taunted Rushu, the king of the demonic Shushus and one of the most powerful and omnicidal beings in the setting. Fortunately Rubilax invokes the Rush right before Rushu is about to incinerate Sadlygrove for his impudence.
On one episode of the animated series of Street Fighter, as Guile and Blanka are in Iraq, some of the people there call him a monster and throw rocks at him. Yes, that's exactly what you want to do to a big green creature with electrical powers and anger issues!
Peter visits Australia and during a walk, he comes up to a sleeping crocodile. He starts poking the crocodile with a stick, yelling, "Wake up, sleepyhead!" Subverted when after a few pokes, a koala flies out of nowhere and latches on to Peter's face.
Aang is a kid, so it's understandable that people might not think much of him. A much less justifiable example occurs between Avatar Roku and Fire Lord Sozin. Roku has finished his Avatar training, meaning he is straight-up the most powerful bender on the planet. Sozin had the nerve to start his country's war on the rest of the planet while Roku was still on the clock, and even acted like Roku should be working for him. Then he attacked Roku when Roku shunned him. Needless to say, a hilariously one-sided beatdown ensued, leaving Sozin minus a palace.
Seen in flashback in "Avatar Day", with a warlord trying to bully Avatar Kyoshi into surrender. When Kyoshi flexes her muscles (breaking off her village's peninsula from the mainland, forming Kyoshi Island), the warlord dies because he's too busy bellowing threats and insults to notice he was now standing on an unstable cliff. (His actual army retreated the moment Kyoshi went into action).
Related to the above examples, a notable (non-flashback) invocation of this trope comes up in the first episode of the second season, "The Avatar State." An Earth Kingdom General tries to help Aang reach the eponymous Super Mode, and when everything he tries ends in failure, he resorts to pushing his Berserk Button i.e. threatening Katara. It ends about as well as you'd expect it to, and the fort where it happens gets smashed to pieces.
Ling Ling from Drawn Together gets abused by the rest of the housemates in some episodes...completely forgetting that the little Asian rat is perfectly capable of ripping them apart easily if he wants to in order to have sex with their skulls. Xander learns this the hard way in one episode.
On Squidbillies, what is Early Cuyler's response to being declared a protected species? Get drunk and pick a fight with a jaguar.
Early: More like a faguar!
In the Ben 10: Ultimate Alien episode "Nor Iron Bars a Cage", a prisoner named Trukk tries to push around Ultimate Kevin, completely ignoring the fact that Kevin is A) bigger than Trukk, and B) breaking rocks with his bare hands. Lucky for him, Kevin was not really interested; otherwise Trukk would have ended up killed rather than just getting beaten up.
Amusingly enough, this isn't the first time Kevin is on the receiving end of this trope. His Freudian Excuse in the Original Series was all about him getting bullied and called a freak for having the ability to absorb energy and shoot electric blasts. You read right: some kids apparently believed it was a good idea to insult and harass a Psycho ElectroCreepy Child.
Amusingly averted by The Men in Black at the beginning of The Windening Gyre, who prove remarquably Genre Savvy when asking Ben to come:
MIB: Standard operating procedure is to show up unannounced, then demand you come with us. But we know we're dealing with Ben Tennyson, so we're asking. Would you please come with us?
Then there's Will Harangue, who is Ben's J. Jonah Jameson, who devotes his life calling Ben a menace, even though if that were true then Ben would have gone alien and turned him to paste ages ago.
One episode of The Looney Tunes Show features Gossamer getting bullied by his classmates. Though wishy-washy at that point in the episode, Gossamer is nevertheless an eight-foot tall hulking monster that could easily play basketball with his entire class (with them being the ball!)
Predaking: Strike me again, and I will bury that rod in your spark.
He still hasn't learned his lesson, as he repeats the same with the slightly smaller Skylynx and Darksteel. Again a literal example, since Skylynx is too a Cybertronian dragon. By the end of Predacons Rising, Skylynx and Darksteel are allied with the aforementioned Predaking, and it's not clear if Starscream will survive the result.
Right after Lucas has seen a Fixed Idea, a near nine foot tall Frankenstein's monster-like man, tear through his wall in Cyber Six, he figures he can take it in a fight. All in all, it's probably his least finest moment in the entire series.
Though admittedly he's desperate to save his sisternote he's being blackmailed into capturing her, the private investigator Yashimoto tries to capture Cyber Six with nothing more than a grappling hook staff thing. Keep in mind this is after he's watched her leap building to building. The only thing that saves him from the beating of his life is that Cyber Six takes a third option and teams up with him to save the hostages.
The page quote is thanks to Mr. Candy from Beavis And Butthead. Keep in mind this guy was an even match for Mr. Van Driessen, and this time around he takes a swing at Mr. Buzzcut. Cue army snare drums and the beating of Mr. Candy's life.
Like in the original movie, Adonis from the TV series of Hercules doesn't realize the danger in bullying someone who can throw a mountain at you. It finally catches up to him when he antagonizes Gaia, who nearly kills him before he manages to appease her.
In the Daffy Duck and Porky Pig cartoon, My Little Duckaroo, Daffy (as The Masked Avenger) repeatedly sees clear evidence that Nasty Canasta is far stronger and tougher than Daffy is, yet he still challenges Canasta to a fist-fight. After Canasta bursts his shirt clear off merely by flexing his muscles, Daffy still persists in accusing Canasta of being too chicken to fight, albeit with a look on his face which says "oh heck, I'm going to die."
In American Dad! Stan does something very very similar to a The Simpsons example above. After searching for the perfect Christmas tree, he falls off a cliff and dies, with his family waiting in the car. Yet his car keys are in his pocket, and they are in the middle of nowhere freezing to death. Stan after losing a trial to determine whether he should be brought back to life, steals a gun that can kill Angels, bursts into God's office. And (Despite being a devout Christian himself) threatens to kill God if he doesn't bring him back to life and save his family. Though subverted, as God doesn't punish Stan (Aside from a sharp telling off) as he is touched that Stan cares about his family that much to do something so idiotic and blasphemous.