In Men In Black, the MIB have the technology to produce "quickclones" that function as perfect copies of the original. The downside? After a few hours they start spitting Word Salad and melt into goo.
Jade from Jackie Chan Adventures once used magic to make a copy of herself to get out of her chores so she could go with Jackie to fight the bad guys. Not only did Jade2 sneak along (because that's what Jade would do), but Jade's duplication spell was imperfect and her clone started making additional clones. Before you know it, there's thousands Jades running around.
In Alienators: Evolution Continues, one of the uncontrollable mutations Wayne sported was uncontrollably and continuously cloning himself. While initially amusing, it is soon discovered that with each splitting the copies have less and less of Wayne's original DNA, threatening to cause yet another alien outbreak.
In Xiaolin Showdown, The Ring of Nine Dragons can be used to split the wearer into up to nine copies of himself. The catch is that the duplication process spreads his skills and intelligence thin across all the copies. Continued practice with the ring did allow the user (notably, Jack Spicer) to overcome this weakness, though.
One of The Simpsons Treehouse of Horror specials had Homer do this using a magic hammock (which the clones themselves end up using, causing them to degrade in quality until one of them comes out as PeterGriffin, until they all run off a cliff when baited by a giant donut). The twist was that it wasn't the original Homer that survived at the end. The real one was the first over the cliff, despite hearing Lisa tell everyone the plan.
In one of the Pinky and the Brain comics, Brain fires Pinky and uses a duplicator device to make a copy of himself. The copy refuses to assist, however, and steals the duplicator, creating a copy of himself, and so on ad nauseum until Brain manages to "cancel out" all the copies. Pinky, of course, returns, over the course of the adventure ... and the last panel depicts lots of copies of Pinky, which presumably gets dealt with off-camera.
An episode of the actual show was similar. Brain tried to make clones of himself to teach a catchy dance to the world, and Pinky wound up being accidentally cloned and distracting the Brain clones with his own dance.
Animaniacs had the episode "Astro-Buttons," where Mindy accidentally gets duplicated at the end.
The Brak Show had an episode based around this, where Brak and Zorak spend all weekend playing video games, and then when the family decides to go out to Brak's favorite restaurant, Brak and Zorak are told they can't come because they didn't finish their homework. After the parents are gone, Zorak talks about needing a time machine, and Brak reveals that Thundercles left him the key to his Time Shed. They go back to the beginning of the weekend to warn their past selves to do their homework, but get caught up in video games until they're called down for dinner, causing Brak to panic as he realizes he's out of time. This repeats many times until his room is completely filled with copies of Brak and Zorak, at which point they decide the only viable solution is to go back in time and prevent the invention of homework. They also inadvertently prevent Brak's favorite restaurant from ever being made, but the one that appears in its place is pretty good too, so it all works out in the end.
Ben 10 gained a duplicating alien form named Ditto. Anything that happens to one Ditto is felt by all of them. Given what happens to the Stinkfly clones, if one Ditto is destroyed, the rest will presumeably follow.
In the Re Tool into Ben 10: Alien Force, the form called "Echo Echo" takes this role (minus the part about feeling each other's pain), but combines it with a weird look, a creepy voice and sonic powers.
Batman: The Animated Series uses this in the Riddler episode "What Is Reality", where he controls a virtual reality universe that follows his every whim. In the end, Batman faces off against the Riddler, who demonstrates his mastery of the domain by duplicating himself. Batman realizes he can do so as well, and the two get into a ridiculous arms race of clones. Eventually the Riddler's consciousness is spread too thin for him to maintain the simulation, and it collapses, with Riddler's mind still inside.
In an episode of The Batman, an old friend of Bruce Wayne's makes a quantum duplicator, immediately resulting in an evil twin of himself who locks up the original and becomes the super-villain Everywhere Man, who steals things and replaces them with quantum clones so no one can tell they're even gone. It takes a literal army of him to take on Batman and Robin (who were armed with the less-stable prototype duplicator), and the Dynamic Duo last long enough to take advantage of the device's one flaw: the clones eventually start to exhibit free will. The clones turn on Everywhere Man when Batman reveals he has neither the ability nor the intention of allowing them to exist after the battle, forcing Everywhere Man to dispel them all. When Everywhere Man says he can just create another army, Bats tells him he can't win because the end result would be the same. This may have just been a bluff to distract Everywhere Man, so the guy he was cloned from could sneak up, grab the duplicator, and dispel him.
In an early episode of The Fairly Oddparents, Timmy wishes for "a ton" of copies to do chores. His Literal Genie godparents divide 2000 pounds by his body weight to get 42.5 clones (the .5 is rendered as a half-sized Timmy). The result follows the second case of the trope, so that Timmy has to get all the clones rounded up into a room and wish them away before someone sees more than one Timmy at once.
In an episode of The Adventures of Jimmy Neutron, Jimmy cloned himself, but mixed it up somehow. Each clone was a different aspect of himself (his Romantic side, his Cool side, etc.). This, of course, included an Evil Twin. Hilarity Ensues. However, even by the end of the episode, the evil twin remained, and eventually got a full-length episode where he served as the main antagonist before presumably dying (and not just in the "absorbed back into Jimmy" sense either).
Danny Phantom has the main character using one of his dad's "Fenton" devices to split himself in two: one to fight ghosts around the clock, the other to goof off. Of course, his personality splits too, one is The Ace and one is a slacker.
Also, form duplication is a special trick possessed by particularly powerful ghosts, Vlad being able to split himself into four normal forms, or hundreds of shadow forms. At first, Danny could only do it through the use of a power-enhancing Humongous Mecha (the two times he tried before that, he respectively only grew a second head, becoming a cyclops briefly when they re-merged, and became a Body Horror for a bit), but he managed to pull it off on his own during season three... the reason he didn't use the power more is the fact that it was STILL hard to do (the duplicates fused back with him after an attack), and seemed to require a lot of concentration and effort, showing that he needs more practice.
In W.I.T.C.H., both the animated series and original comic version, the guardians can use the Heart of Kandrakar to create soulless slave clones of themselves known as Astral Drops. Normally the use of Astral Drops is rather innocent, but have occasionally led to big problems, most notably in the animated series episode "H is for Hunted" (Nerissa turns an Astral Drop into a person with real feelings and emotions) and the third volume of the comic book (Astral Drops rebel and wreck girls' romantic lives).
It gets pretty messed up in the comic, when the Astral Drops suddenly gain independent souls, causing the original girls to be haunted by the spirits of their copies whenever they absorb them. The oracle eventually decides on turning the Astral drops into independent people with their own bodies, appearances and identities, which, however, leaves the girl's without cover-ups for their missions.
In Transformers Animated, Starscream gains the ability to make clones of himself that each possesses one facet of his personality. There's a sycophant, a compulsive liar, a coward, an egomaniac, and an Opposite-Sex Clone ("You Do NOT Want To Know," she says... though she seems to be the part of him that's actually competent). Upon getting to know his clones better, he realizes one thing: "This is gonna be a long orbital cycle."
The toyline and second Allspark Almanac add two more: Dirge, who represents Starscream's greed, and Thrust, who has Starscream's envy. Both were made by Swindle as bodyguards.
Subverted in one episode of Care Bears, where Shreeky gets her partner/lackey, Mr. Beastly, thrown out of No Heart's Castle for something that was her fault. Shreeky ends up having all of Mr. Beastly's menial chores foisted upon her, and comes up with the genius idea to magically clone herself. She introduces her legion of Shreekys to No Heart, each with its own responsibility...but when she explains that the last one's job is to take the blame for making messes, the Shreekys start bickering to the point that No Heart declares that "one Beastly is better than five Shreekys any day! Get them out of here, and get Beastly back!" (Though since this means she's gotten out of doing chores, she still got what she wanted anyway...plus a little catharsis out of vaporising her misbegotten legion of clones, who immediately start bickering again over whose genius plan it all was.)
In an Adventures in Care-a-Lot episode, Grumpy uses a machine to create a clone of himself to help him build his latest invention, but the clone wants nothing to do with Grumpy's original blueprints and creates a clone of his own. The two clones kick Grumpy out of his own workshop, but when Grumpy gets back in (with some help from the others), he finds the clones are sick of each other, and they willingly go back into the machine.
Time Squad, "Day of the Larrys": Sarcastic Robot Buddy Larry 3000 decides to build a duplicate of himself to help around the station. The duplicate decides to build another duplicate, and so on.
Lady Redundant Woman, from WordGirl, gained the ability to do this from - get this - a photocopier accident. She literally merged with the copier. The clones turn into paper when hit.
Rolie Polie Olie: This was the plot of the episode "One Olie, Two Olie, Three Olie".
One Johnny Test episode had the title character notice his super-intelligent twin sisters pull the duplication act in order to spend their afternoon ogling their hunky neighbor instead of cleaning out the garage. So he uses their duplication machine to get out of mowing the lawn... and, of course, leaves it on so that it makes a total of 100 clones tearing up the lawn. And Dad, who quite specifically told them not to duplicate themselves like last time, is only 10 minutes away from home...
In one Tiny Toon Adventures episode, Plucky doesn't do his homework, so he builds a time machine and goes back in time to the start of the weekend, where he meets himself. Plucky B takes the time machine and goes forward to Monday morning, where he shows it to Buster and Babs, and while playing with it, they accidentally end up in prehistoric times, where they meet their ancestors.
Happens in the Lilo & Stitch: The Series episode "Dupe", where one of the experiments has the power to duplicate anything multiple times. Originally, the protagonists think that this is a wonderful way to get everything they want done at once, but eventually they realize that every duplicate reduces the collective power of everyone who has been cloned, original included, to 1÷(number of copies). It becomes Chekhov's Gun later in the episode.
In Kim Possible, the Wego twins' power is to create more of themselves.
The Spliced episode "Clones Don't Care 'Bout Nothin' Either". Unusually, they actually succeed in taking over the lives of the original.
Multiple Santa and his electrically generated Santa Clones from The Tick.
In Teenage Mutant Ninja Turtles, Donatello is tired of fixing things, so he create a clone of himself. The clone refuses to work and a cloning glitch makes him stronger and smarter than Donatello. He sides with Pinky McFingers, creating millions of cloned rats planning to loot the city.
Another episode (Appropriately called 'Split Personalities') has a molecular splitter the boys invented inadvertently divide Candace in two- one obsessed with busting, the other obsessed with Jeremy Johnson. After some confusion, the brothers manage to corral both Candaces and merge them, but not before briefly splitting the two into more Candaces!
Another episode has the boys create Phinedroids and Ferbots, who not only complete all the boys' projects but also start projects of their own.
Beast Boy can accomplish this by turning into an asexually reproducing lifeform and just splitting. In the comic book continuity, he is shown to have the potential to gain this power as an extension of his shapeshifting powers but isn't confident enough to employ it just yet (although some Flash Forwards have shown future versions of Beast Boy being able to more or less become a one-man green stampede).
This is the power of villain Billy Numerous, hence the name. All the Billys appear to have the same personality, and since Billy is a bit of a hick, he fights with himself a lot.
This was also the plan of the aquatic villain Trident, who considered himself to be the ultimate life form. Beast Boy solves the problem by asserting that only one of them can really be the best, causing them all to fight amongst themselves.
Seen in the Futurama episode "Benderama". Professor Farnsworth invents a machine that makes two smaller copies of any object. Bender uses it on himself to make two smaller clones to do his work for him. Then each of the clones makes two clones. And those clones make two more clones, and so on until the Earth is threatened by a Grey Goo of microscopic Benders.
In Marvel's licensed Ren & Stimpy comic, the Commander Höek and Cadet Stimpy story "I Scream Clones" features Stimpy acquiring permission from Space Command to clone himself in order to keep up with his shipboard duties. Predictably, the proliferation of Stimpys threatened to drive Ren mad....until he realized that he could simply clone himself and create an army of Rens to smack the stupid out of the Stimpys.
One of the powers The Powerpuff Girls use is "copycat," in which they make multiples of themselves. They use it first in "Forced Kin" against an alien spacecraft but they are outwitted as the spacecraft makes multiples of itself as well. They do it again in "Nuthin' Special"—Buttercup tries to show it as her special individual power (one of several), but Blossom and Bubbles match her.
Danger Mouse had the episode "Tiptoe Through the Penfolds". Baron Greenback creates a magnetic molecular molder with which he plans to create 1,000 clones of himself so nobody would be able to catch the real Baron. On a test run, he creates a series of Penfold clones, but the off switch breaks. As a result, a million Penfolds virtually flood London.
Wow! Wow! Wubbzy! had the episode "Too Many Wubbzys," where Wubbzy uses a machine to create clones of himself.
My Little Pony: Friendship Is Magic "Too Many Pinkie Pies": Pinkie Pie is frustrated because she sometimes have to choose between different fun things that her friends are doing at the same time. She uses a magic pond to clone herself. Then the clone decides to clone itself, too, and so on. Pretty soon Ponyville is overrun with Pinkies and Hilarity Ensues.
The Gravity Falls episode "Double Dipper" has Dipper making clones of himself with a strange copier machine. Avoids the Evil Twin trope because all of them are nice, but they insist on his carrying out a pre-arranged plan and try to stand in for him when he doesn't go along. There is also a damaged clone created by a paper jam. They have very little Cloning Blues even though they know they are temporary and can be destroyed by water.