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Genetically altered humans and/or animals, which often contain extraordinary superpowers. Prevalent in the Sci-Fi genre.
Born with Super-powers despite Human Ancestry Si-fi and fantasy films often want to give relatable characters, but are unable to explain how they gained extraordinary abilities. Most mutants are generally due to a new gene that appears in only certain humans.
The super-powered individuals of this universe are given powers through the "x-gene." It is seemingly random, as mutants can be born to human parents, and can have siblings who do not have the abilities. Something about the X-gene causes reality warping powers, though the affect it has varies from mutant to mutant. Mystique, for example, can shapeshift while Storm can manipulate the weather.
Harry Potter Wizards
The wizards of Harry Potter obtain reality-warping powers in a way similar to the X-Men. Wizards can be born to humans, and humans can be born to wizards--though it is more likely that wizards will be born to wizard families. Unlike the X-Men mutants, the Harry Potter wizards all have the basic same powers, though their skill and aptitude may vary.
Star Wars Jedi and Sith
The Jedi and Sith powers are caused by a genetic condition that causes much more "mitochlorians" (an unexplained substance) in their bloodstream. They all have the basic powers (increased reflexes and agility), though the more mitochlorians a person has the more powerful they are (some are able to even fire energy blasts). Mitochlorians can be found in many different races. Thus, a Jedi may have additional powers due to being from a race that is already gifted (an example would be Darth Maul).
Genetically-altered Humans Some stories feature characters who were born ordinary humans but were genetically altered from an outside event into something different.
Sam Raimi Spider-man Metahumans
In the Spider-man universe developed by Sam Raimi, the superhumans have all been mutated by radiation, though the way they received it and concentration they absorbed changes the affect. A radioactive serum causes the increased agility and strength of the Goblins, a nuclear experiment in a sandbed caused Sandman, a bite from a radio-active spider caused Spider-man, and so on.
The Mutated Humans of The Avengers
Radiation absorbed into the blood caused several of this series characters to gain powers, including Captain America and the Incredible Hulk. The radiation was caused by a type of cosmic energy that is harnessed by Iron Man in his repulsor beams and is genetically encoded in the alien Thor, though neither of them count as mutants.
Many of these characters (including the Teenage Mutant Ninja Turtles) are mutated animals.