Funny Valentine of Steel Ball Run can visit alternate dimensions and bring back copies of himself. Since the copies all have his exact same personality and memories, and because there are infinite worlds, Valentine is almost invincible.
In Mahou Sensei Negima!, Negi attempts to make a single copy of himself using a traditional Japanese magic that animates a paper doll, with which he is unfamiliar. Eventually he succeeds, but all his previous (bungled) attempts also animate, and Hilarity Ensues as the small crowd of defective Negi-copies run around amongst his students, just as they decide to make him the object of a kissing competition. Later, in the manga storyline, Negi experiences the first day of the Mahora festival multiple times via a Time Travel device, and fails to entirely keep the secret of what he's doing from his students.
Kotarou and Kaede can use (the by-now mandatory) Ninja self-duplication techniques; Kaede notably starts off a beautiful Mundane Utility sequence by splitting herself into 14 copies in order to forage for edible wild plants really fast.
Negi has also learned how to make clones out of lightning. Actually, he could always do that—now they're actually convincing.
In episode 23 of Sgt. Frog, Keroro tries to use the (malfunctioning) Kero-Ball to fix one of his Gundam model kits, but accidentally activates the "Copy" function instead, which results in hundreds of Keroro clones infesting the Hinata house and the base. He plans to use these clones to help him take over the planet, but they're all as lazy and goofy as he is and would rather slack off. What's worse, he later learns that unless he gets rid of the clones somehow, the Kero-Ball will overload and all the Keroros (including the original) will vanish.
However, this example above is directly lifted from the main plot of another series, Shichinin no Nana/Seven of Seven (one of the recurring characters in SoS is from Keroro, so it goes both ways). The seven Nanas, however, are all considered separate people, unlike many examples on this page. All we can say for the girl's love interest is, you poor lucky bastard, getting seven girls who all want you (and likely aren't afraid of sharing)...
In Naruto, this is known as Kage Bunshin No Jutsu (Shadow Clone Technique), and the title character uses this as his primary battle technique. Other characters use similar techniques, but can't quite manage it on the same scale as Naruto himself, who can create upwards of a thousand copies of himself. Sadly, it rarely helps. In the Naruto world, Conservation of Ninjutsu applies to your own clones.
It sometimes helps a lot, but going up to Conservation of Ninjutsu levels means it's probably a distraction or temporary Red Shirt Army of himself. After the Time Skip, he shifts toward uses small numbers of clones as decoys rather than a Zerg Rush of huge numbers of them. Clones to help him execute his big mojo attacks are very useful regularly.
As a side note, his clones can also function the same as Jamie Madrox from the aforementioned Marvel Universe in that any experience his clone has will be absorbed by Naruto upon dispersion, so he can learn new abilities faster, but he also absorbs any mental strain experienced. Thankfully, he doesn't have the Evil Twin problem in this case, but he does sometimes accidentally get into fights with himself before remembering he can just end the technique.
This is more a "conservation of chakra" issue. Each of the Naruto clones can still execute all of his techniques and retains all of his expertise (which, because Naruto is canonically an Idiot Hero, is not necessarily a lot, especially in the beginning) ... it's just that they're not as super-powered as he alone would be. Consider that Naruto is stated to have access to something near 100x the amount of chakra as his teacher Kakashi - who's fairly powerful himself - and boggle at the thought of it.
It's revealed in the Chunin Arc, that creating a '____ clone' requires expending a significant amount of chakra. It is implied that there are different levels of chakra required to create a clone. Up to six illusions that merely copy the caster can be used even when said ninja is on the verge of collapse. Creation of a complete clone involves dividing chakra evenly between the clones. Clones created using elements or physical objects (water, paper, etc.) cost less than creating them out of scratch, with the trade-off of needing to have enough of the element in question present (for example it's relatively easy to make water clones if you're near a river, but problematic if you're in the desert). The latest arc revealed that chakra is evenly transferred between clones, so a more recent strategy involves having a few clones store up chakra while the rest fight: when Naruto runs out of chakra, a clone dies, and Naruto gets his health fully restored. The limits of this haven't been completely tested, but it seems he can enter 'Sage Mode' indefinitely (barring the physical strain of the ability) and can spam his highest level techs while in that form.
In Nurse Witch Komugi, Komugi magically cosplays as Ken the Eagle from Science Ninja Team Gatchaman in a desperate bid to defeat her Transforming Mecha-controlling Ninja Maid enemy (who was cosplaying as Tekkaman)... and is soon joined by the rest of the Science Ninja Team, who are also cosplayed Komugis. Another Komugi later appears as The Professor. Her sidekick had no idea she could even do that, but Komugi plays it off like nothing at all.
Treated with much more seriousness in Komugi's parent series, The SoulTaker, with Kyosuke's sister Ruina having created various "Flickers" of her soul to throw off her pursuers. They all look different and a good chunk of them don't even know they're Flickers to begin with.
The hero of the manga Akumetsu is a terrorist clone army, and manages to make this ridiculously cool. His trademark mask blows his head off when he dies, concealing this slightly (slightly) from the authorities, and also transmits all the memories and consciousness of the dying member to his base in space, where they make a new copy. Kind of makes a cheat of the 'I'm willing to die to wipe out evil' thing.
This is a technique sometimes used in Dragon Ball, originally by Tenshinhan, albeit in filler Piccolo (And once Krillin, oddly enough) loves using it as well. Tenshinhan originally used it as a combat technique, but this became less useful as the character got stronger due to each clone having a fraction of the original's strength. Piccolo normally uses it for training purposes, allowing him to spar with himself.
Subverted with the ninja Murasaki. He claims he can create four identical clones, each as strong as himself; in fact, he's one of a set of quintuplets.
Ninin Ga Shinobuden has Onsokumaru attempt to use a cloning jutsu. He succeeds, but ends up locked in an "epic" battle with the clone. Who poofs out of existence anyway when the spell duration runs out.
Konatsu the Kunoichi from Ranma ½ has a technique that allows him to do this.
The Manga Adaptation of The Legend of Zelda: Four Swords is all about this: Link is split up into 4 different Links (optimistic and childlike Red; aggressive and over-confident Blue; controlled and intelligent Vio(let); and the (perfectly regular) brave and virtuous green Link) plus one Shadow Link, who came from the Shadow Mirror and serves as an Evil Twin. The five Links superficially differ only by the color of their clothes (and hair, in Shadow Link's case). In the manga pages themselves, they also have their eyes drawn differently (Green: Normal and Clear; Red: Big and Wet; Blue: Smaller irises and Edgier; Vio: hyper focused and empty irises; Shadow: either empty or colorless irises), on the colored illustrations, however, their eyes are all the same as well.
In one episode of The Adventures of Mini-Goddess, Urd is babysitting some rats, and runs into a situation where she is asked to do three things at once. She however wants to play craps. She then makes two clones of herself, however all the clones wind up wanting to play craps as well. As you would expect, no actual work got done.
Mizore from Rosario + Vampire can create "ice clones" of herself and her friends, which seem to be able to operate independently, though they don't last long. They're quite fragile as well, so she doesn't use them as backup combatants.
Code:Breaker: Heike can split himself into 100 clones as a result of his light powers combining with his superior intelligence.
DoraemonThe Movie "Nobita and the Kingdom of Robots" has the titular character Doraemon fighting for his life in an arena. So what does he do? Fill the arena with clones so the opponent can't tell which one is the real one.
Ryoko and Ryo-Ohki of the Tenchi Muyo! OVA can do this, but they've never done it in combat - Ryoko used hers for role-playing while Ryo-Ohki wanted carrots.