Dungeons & Dragons: Zig-zagged across editions, with 3.5e providing the most options for accomplishing it.
The Fission psionic power and the Body Outside Body spell both let you clone yourself. Through Loophole Abuse, the incantatrix Prestige Class can use the latter to produce a hundred or more clones that last all day, and apart from a bit of feedback damage if they die, they are completely expendable.
The spell Simulacrum creates weaker copies of the target, all absolutely loyal to the caster. Enterprising mages can use this to create a telepathic gestalt of expendable avatars.
The Mind Seed psionic power overwrites other people's minds with copies of the caster's consciousness, combining this trope with Split-Personality Takeover.
GURPS has a Duplication advantage and Clone spell.
The Clarissa Explains It All Game can be played by up to six people, and all of them will be Clarissa Darling. Whoever gets a Driver's License and car first, wins!
The The Honeymooners and many Scooby-Doo board games work the same way, with everyone playing the same character without any acknowledgement of the fact.
Mutants & Masterminds has a Duplication power and includes at least two crooks with the power set. Remlok, a time-traveling thief, summons himself from various futures. The Other Woman has a more conventional duplication power.
In the Adventure! pulp RPG from White Wolf, this is the secret power of Yellow Peril villain The Ubiquotous Dragon. Being a universe where the power scale is rather low, this is not only a very powerful ability, but he also uses it in a much more low key way than most examples on this page. Essentially, every one of his local Co-Dragons is himself, which means they are perfectly loyal and coordinated, and even if you find the body, he will still be there.
In Eclipse Phase, Brain Uploading has become so ubiquitous that there are now more disembodied minds than there are organic bodies to accommodate them. All one needs to do create a horde of themselves is to create duplicates of their minds (in a process called "forking") and then download them into new bodies (either organic or robotic). However, if the forked personalities stay separated from the original for more than a few hours, they start to become separate and distinct people, as their experiences alter their personalities.
The "Mr. LeThuys" in Over the Edge, who are a not-so-secret conspiracy of an old, potbellied, nihilistic Vietnamese man named Mr. LeThuy who had a mad scientist create a retrovirus using his genetic material that would slowly change anyone injected with it into an identical copy of him. His/their goal is to gradually convince everyone else to join him/them, so that he/they could then end the human race and end the chaos of existence. He/they is/are also very convincing...