An episode of the 1980s cartoon has Shredder being jumped by a mugger upon being teleported into Central Park after a long imprisonment in Dimension X. It is one of the few occasions on the show where Shredder actually gets to kick someone's ass.
Another episode has a mugger try to mug the disguised turtles, which is delt with in a similar way to the Crocodile Dundee example shown above. The mugger demands "Give my your wallet!". Leonardo replies "I've got a better idea *draws huge katana blade* give me your knife!"
In one episode of The Powerpuff Girls, a thief — not a supervillain, just a regular, common burglar — actually tries to rob the Girls, because he had somehow never heard of them. Needless to say, it does not go over well, though they couldn't just kick his ass immediately because they didn't want to wake the Professor. At the end of the episode, the thief was heading towards Mojo Jojo's house intending to rob him.
The two-parter "The Call". In an attempt to escape Terry, Inque takes an approaching bystander hostage... who turns out to be Superman. On the whole, not her finest hour.
Something similar also happens in the very first episode, when a group of Jokerz (a street gang patterning themselves after the original Joker) decides it would be a good idea to intimidate a certain old man by saying "We're the Jokerz!" Unfortunately, said old man was Bruce Wayne. Cue the Curb-Stomp Battle.
Jokerz Leader: Don't you know who we are, old man? We're the Jokerz!
A small group of Jokerz harrasses Willy Watt midway through "Golem". They try to put the squeeze on him, but Willy calls out his little friend...
And in "Bloodsport", a lone Joker tries to mug Terry when he's chasing the Stalker — and gets dismissed in an especially pathetic fashion.
Continuing with the Jokerz in a crossover with Static Shock: the Jokerz lure two teens onto their turf... but one of them is Terry and the other one is Static. Uh oh. (Long story short, the Jokerz really aren't too bright.)
In the SpawnAnimated Adaptation, when Angela is first introduced, a couple of thugs follow her into an alley to rape her. Naturally, only she leaves the alley.
In the Fantastic Four cartoon (the one that took place in the Iron Man Hour), a mugger tries to rob a guy in a trench coat with a young woman. That guy turns out to be the Thing. Alicia points out that with Ben, she feels safe walking in the park at night.
"Knight Time" from the DCAU features a Superman/Batman crossover in which Superman had to disguise himself as Batman in order to help Robin (Tim Drake) find out where his boss had gone. At one point, Superman also found it necessary to round up Bane, the Mad Hatter, and the Riddler. The Mad Hatter and the Riddler, who knew they were no match for Batman physically, wisely tried — unsuccessfully — to make themselves scarce at once. Bane, who did have reason to think he might do better, ended up having "Batman" beat the CRAP out of him while the Riddler (detained by Robin) watched in utter disbelief.
Robin: He's been working out.
Subverted in another episode, where Clark notices someone is following him. He turns into a dark alley, and the would-be robber thinks he's got him. But as soon as the person enters the alley, no one is there, and is very confused. Cut to Clark up on the roof of the building next to the alleyway with a slightly annoyed look on his face...
Used nonviolently (but very sadly) in a Russian cartoon, Maska. It's Halloween, and a little pretty girl walks down a street, alone. Then two blokes with huge monster masks jump from the corner and attempt to scare the little girl. The girl first watches indifferently, then she has enough, and tears down her face — which turns out to be a mask concealing her real face, scarier than both monster mask combined. The blokes, horrified, drop their masks and run away, leaving the girl weeping — by their scare they reminded her of her own face.
Kim Possible: During "Graduation, Part 2", Ron, unbeknownst to the Lowardians, comes into control of a very great power, making Warhok and Warmonga's tap-dancing on his Berserk Button a very poor idea. It crosses into Bullying a Dragon when they continue messing with him even after he's taken out all their tripods and thrown Warhok across the landscape.
Transformers Prime has the organization MECH attempt to steal a nuclear device from "an unarmed civilian truck". The Autobots trash the attacking cars, without bothering to transform.
An episode of Futurama had Bender constantly harrassing a thin robot sitting in front of him at the movies. Eventually the skinny robot has enough and challenges him to "fisticuffs". Bender laughs... until the guy transforms into a much scarier form. Turns out he was a professional robot fighter.
In another episode, Fry and Leela are nearly mugged. But Fry is unhurt when the mugger shoots him — it turns out he and Leela had recently developed superpowers, which they then use to knock the mugger around.
Batman: The Animated Series episode "Birds of a Feather" proves that just because Penguin always loses to Batman doesn't mean he is a bad fighter. He is able to hold his own against three muggers before Batman intervenes and defeats all four of them (Batman thought he was with them until it was funnily resolved).
Another example in the series (this does seem to happen often when Batman is involved) was in "Mad as a Hatter", Jervis Tech's first appearance. He hadn't quite become the Mad Hatter yet, but when escorting his date Alice through the park, two muggers accosted them, and he quickly used his mind control devices on them. After doing so, he ordered them to "go jump in the river". While Alice saw that as simply a way of saying "get lost", they actually took it literally, climbing to the top of a bridge to do so. Batman had to rescue them before they killed themselves. (Clearly, if Tech's Start of Darkness had not already begun, this is what truly started it.)
In Invader Zim, Iggins learns the hard way why it is not a good idea to withhold the Game Slave 2 from Gaz. How? She follows him all the way to his house, writes "the game is mine" on the bathroom mirror, appears in the door, steals all the batteries in the house to keep him from getting to the save point on the game, causes the elevator to malfunction when he's still in it, and finally throws him down said elevator shaft.
Humorously in Archer, when the title character attacks an older gentleman in a bar for laughing at him... and gets pinned to the bar by Burt Reynolds, who also happens to be Archer's man-crush.
In The Simpsons, blue-haired lawyer and a pair of goons confront principal Skinner about his student fair's use of Disney's copyrighted "Happiest Place On Earth" phrase. Upon informing Skinner that he's made a big mistake, Skinner calmly informs him that so has the blue-haired lawyer, before telling him they got an ex-green beret mad. He promptly hands them all their asses.
Once invoked with Blue Beetle. Jaime is investigating the disappearance of his friend Tye, when Tye's mother's boyfriend Maurice finds him and throws him onto the ground. Now, Jaime's no pushover...but the one you have to look out for is the Scarab in his spine, who takes the opportunity to whip out his favorite weapon (the Plasma Cannon), and demands that Jaime kill "the Maurice". Jaime, luckily for Maurice, keeps him restrained, averting this trope.
One time, Captain Cold decided to target a bank for a heist, completely encasing about half the street in ice. Imagine his shock when one of the ice walls explode to reveal seven super-heroines, who just happened to be having a bridal shower there. He doesn't even attempt to fight.
In an episode of The Real Ghostbusters, this happened to the Ghostmaster when he came to New York seeking revenge against the heroes. Seeing as the Ghostmaster ranks a Class 11 (according to Who's Who in the Spirit World, which possibly makes him the most powerful ghost ever to appear on the series) the crooks were lucky to escape with their lives.
An episode of The Transformers had the Autobots helping the police catch carjackers by posing as normal cars, waiting to get stolen, then thrashing the hideout on arrival.
During Ben 10's run, Cartoon Network would occasionally show this two-minute shorts during commercials. In one of them, a pair of thugs try to steal the Rustbucket. However, they do so while Ben is hanging around. Needless to say, things do not end well for the crooks.
In Cyber Six a trio of students attempt to rough up Adrian (who is actually the titular Cyber in disguise) for rejecting Lori's advances in class. It's actually lucky for them that Lucas spotted them from the window and decided to intervene to help Adrian.