Los Hermanos of the Global Guardians PBEM Universe has this power in spades. He combines this with Hive Mind, as not only can he create thousands of copies of himself, he shares his consciousness between them. (He is somehow capable of dealing with all the conflicting sensory input, and is capable of handling multiple tasks at once, multiple conversations at once, and so on). At any given moment, he's likely got a dozen duplicates active around the world working in as many different occupations. Anything one duplicate learns, all the duplicates know how to do. And at least two of his constantly active duplicates are married. But only one is an active superhero.
Aryan Nation is a controversial white supremacist superhero (yes, you read that right) who shares Los Hermanos's powers. His powers are so similar to Los Hermanos that the Global Guardian once hypothesized that maybe Aryan Nation was one of his dupes who managed to gain a separate consciousness. (He found out later this wasn't true.)
Posse is a superhero from Dallas, Texas, who can separate into twenty individuals.
The Seven Brothers is a super-strong Chinese hero who can split into seven bodies. He is also a Hive Mind.
Mob Rule, a South African super villain from the same setting, has a similar power. His copies, however, are independent individuals.
Colony, a British super villain, can create a dozen duplicates. Like Mob Rule, his copies are independent.
Saba Devatao, an Indonesia super villain, creates eight duplicates and like Los Hermanos is a Hive Mind. She's an expert martial artist who can flawlessly coordinate her bodies in attack routines that baffle most of her opponents.
Jade (a.k.a. Generator) of the Whateley Universe has the ability to create disembodied copies of herself, complete with personality, that can possess and telekinetically manipulate physical objects. Needless to say, she's finding a lot of uses for them. Like pretending to be the ghost of her — actually nonexistent — older sister so she can attend two classes at once, say...but at least as initially depicted (before individual functions seem to take over a bit), they're still all very much her to the point where she's temporarily devastated when one vanishes without a trace due to another mutant using her own power to trap the loose 'spirit'.
It appears to be implied, in the various stories from Jade's perspective, that the copies are all still her - but they're referred to by different names both so that other people (and, sometimes, Jade herself) can keep track of who is doing what and so that the Pronoun Trouble doesn't get too excessive. Plus, a large part of Jade's secret hinges on her posing as her own sister. Unfortunately, recent events may also have implied that the whole thing may not be having the best effect on her sanity. It's really not good for you to possess an athame that's been used by an evil sorceress who routinely uses it in some very bloody rituals...
Aurora in Trinton Chronicles has the ability to create duplicates of herself out of energy and each one has her personality making them essentially her at heart. The duplicates are only linked to her in the fact that she feels their deaths or pain but nothing else. They are created from energy and must verbally impart any knowledge they learn to her. They also all seem to be 'aware' of their meager existence, going so far as to protect the real Aurora from various attacks at the expense of their own forms. Once dismissed they just dissolve into energy. Theory is that each clone is a part of Aurora given form but that has yet to be proven.
In one of the comics at the Heroes website, immortal villain Adam Monroe encountered a duplicator with this power during the Revolutionary War. The duplicator was unable to overcome Adam's Healing Factor, and no matter how many doubles Adam killed, more could keep coming as long as one of them survived.
Of course, this doesn't count the original Insano that was running around, as well as all the various characters played by Spoony, like GordonRamsay, Ultimate Warrior, Terl...
The Angry Video Game Nerd once made three clones of himself to demonstrate how a video game he was reviewing had a four-player option, since no one would have wanted to play the game.
The SCP Foundation has SCP-1157, AKA the Bifurcated Man. Once every 4 weeks, at precisely 3:08 AM EST, all instances of him involuntarily divide into two new duplicates of himself. Also, Doctor Bright, through seemingly a side-effect of the body-surf style immortality caused by SCP-963, generates new versions of himself whenever somebody wears SCP-963 for more then thirty days.