Magic Genetics

Now, you want to give this character really cool superpowers. However, you need to justify it. So you say that it's a result of genetic mutation caused by a Freak Lab Accident.

However, could that really work? Let's say you want this character to be able to fly. But without wings, where would the propulsion come from? Let's say you want this character to be able to grow 100 times their size. What about the law of conservation of matter? (Not to mention that even if it was possible, the person would probably die from insufficient amounts of blood.) Let's not even get started on creating fire out of thin air...

Many writers don't know (or deliberately ignore) that genes are only responsible for protein synthesis. This is when said writers give genes the ability to alter the very laws of physics (or other universal laws) - or at least the ability to do things that would be impossible for a human. Lego Genetics is often involved, as well. Extra fail points if the writer ignores the necessary secondary powers needed for the Functional Magic to actually be functional, such as Photographic Memory for Voluntary Shapeshifting etc.

If the writer wants to firm up the science, they might say that the genes merely construct nanoscale Applied Phlebotinum in your cells which acts on "quantum forces not yet discovered" or some other Hand Wave, but it's still really Functional Magic given a pseudoscience gloss-over.

Some types of superpowers being caused by genetics are plausible. Super Strength could be from extra muscle mass or more efficient contractile cells (but you still won't be strong enough to bend girders bare-handed), low-level Super Speed would be a snap as natural human neural impulses and reaction time are notoriously sluggish (slower than sound, in fact) and could easily be sped up by increasing conductivity, claws could be some sort of bone growth or modified keratin, and there are animals that use electricity as a weapon, can stretch and distort their bodies, or have a Healing Factor or Super Senses. While you can't become an invisible man, chromatophores in the skin could give you super-camouflage. Etc.

Genetically-based Psychic Powers are automatically a subtrope of this, as are any Witch Species. Characters who are Randomly-Gifted usually don't gain their powers from genetic sources, or in combination with other non-genetic factors.

A subtrope of You Fail Biology Forever, Art Major Biology and Required Secondary Powers. See also Superpowerful Genetics, Bio Augmentation.

In Superhero stories, usually considered an Acceptable Break From Reality due to Rule of Cool.

Comic Books

 * Most mutants in X-Men such as Storm have the ability to use physically impossible powers as a result of their mutation. Sometimes, they all come from a mutation of a single gene. Justified in-universe via experimentation on proto-humanity by a race of Sufficiently Advanced Aliens. It's the reason freak lab accidents can give normal humans superpowers in the Marvel-verse, the infamous "x-factor"/"mutant gene" serves to makes the activation of these powers a natural part of the mutant's biology.
 * Certain villains in Spider-Man also have these kinds of abilities. Spider-Man himself sort of doesn't count as he "does what ever a spider can..."
 * Attempted to be Justified in Ultimate Fantastic Four, at least with Mr. Fantastic and the Human Torch. Johnny's powers come from his nuclear fusion, using his body as an energy source. Reed is able to stretch and not crush his organs because all he has in the way of organs is a colony of symbiotic bacteria who take in food and air and give his body nutrition. Their origin is justified as well now too, as their powers are not from cosmic radiation anymore, but rather from swapping bodies with a double from another universe. He should just pray he'll never catch a disease that requires treatment with antibiotics...
 * The Meta-gene of DC Comics. A single gene that provides every possible super-power. Various Human Aliens like Superman, the Legion of Super-Heroes, Martian Manhunter, etc. also attribute their abilities to genetics-- Transfer their DNA into a human, and that human becomes super-powered.
 * Wildstorm's The Authority has Apollo, genetically engineered to fly and fire solar blasts. The "gen-factor" of Gen13 and its spinoffs. WildC.A.T.S. get their powers from alien DNA.
 * In Strontium Dog, Johnny's mother gets caught in a fallout shower while eight months pregnant with Johnny; as a result, Johnny's eyes mutate to be able to emit alpha particles, which gives him X-Ray Vision and limited telepathy. Not only is this biologically impossible, but alpha particles do not work that way! In fairness, however, Johnny is an exception; 99.9% of the other mutants are just disfigured, with the lucky ones getting extra body parts.

Literature

 * A comprehensive list of Mutants who develop Psychic Powers in a post-nuclear setting could crash this server.
 * The Maximum Ride novels have children who are "genetically engineered" to have wings. And occasionally other New Powers as the Plot Demands. Weirdly, it is implied that the early powers that they spontaneously develop were also engineered into them, to help them fulfill their purpose to "save the world" or whatever. In the fourth book though, Jeb comments that they seemed to be randomly mutating and developing powers on their own. Which first manifests with Nudge getting magnetic control.
 * Skulduggery Pleasant has magic running in families, to the extent at least one particular type from a particular set of ancestors apparantly manifests 'in the blood' so to speak.
 * Deryni powers are genetic, though most Deryni must be trained in their use. The trait is described as a dominant one (only one parent needs to be Deryni to produce Deryni offspring, and eggs with the trait are hardier and more fertile). Certain bloodlines, including the Haldanes, also carry the variant trait that permits assumption of the powers and the knowledge to usethem without training.
 * J.K. Rowling has stated that there was a Magic Gene involved in wizarding capabilities. This gene could also be present in other magical species. It can remain in a bloodline for generations before manifesting in muggleborns. The inverse is also the reason for squibs.
 * This also doubles as Hollywood Genetics, since the gene is clearly defined as "dominant", but dominant genes cannot skip generations and squibs are much rarer than they should be.
 * The gene is, itself, magic, so can presumably do whatever it likes.
 * Wild Cards, full stop. Apparently a virus containing psionic aliens' DNA can do anything.
 * Many writers wishing to dramatise a transformation between human and animal forms choose to describe a molding-type process, as opposed to a puff of magic smoke. Faces lengthen, ribcages change shape, teeth sharpen - all ok. And then a joint turns over. All mammal joints actually are present in the human form - as the heel of the foot being the equivalent of a hock. No turn-overs would need to ever happen. Prevalent in Harry Potter Fan Fiction.
 * According to Word of God, Magyk in Septimus Heap has a genetic basis, which is why Princess Jenna has no Magykal powers, unlike her adopted siblings..

Live Action TV

 * Nowhere on television is this trope in effect more than Heroes. Apparently everyone's power, from regeneration and invisibility, to clairvoyance and time travel, are just a matter of having the right DNA.
 * Stargate SG-1 has a Goa'uld Mad Scientist mutating humans to give them Psychic Powers in order to create a super-host.
 * Mr. Spock's ability to mind-meld comes from his Vulcan genes.
 * All powers in Mutant X come from genetic experiments conducted by Genomex and . These powers include generating electricity, density manipulation, throwing energy balls, time travel, etc.
 * Ditto for Painkiller Jane. Yes, time travel included. Especially ridiculous since.

Tabletop Games

 * GURPS Bio-tech has a section on magical genetic engineering. Along with replicating scientific possibilities, it allows genengineering ability to cast any spell into a not-yet-born child. It is cheaper than making a ordinary magical item, but risks making a Phlebotinum Rebel.
 * Otherwise, it tries hard to avert this trope. For example, angel-like wings can be genengineered, but don't give ability to fly an 1 G. They might be useful at lower gravity or in a space habitat, through.

Video Games

 * Bioshock is made of this trope: The game establishes that in-game Plasmids and Gene Tonics work by rewriting their user's genetic code from scratch to allow for fantastic new skills...such as being able to summon fire, lightning, and worst of all, bees from your hands.
 * A recurring theme in Star Ocean: Till the End of Time
 * Two words: Symbological Genetics. Tinkering with genes can give you magic powers.
 * Star Ocean 1: The Climax Boss and Final Boss were created through genetic engineering to survive a Mordor planet. There is also a species that naturally posesses magical genetics.
 * Star Ocean the Second Story: The main villains were a group of people who were granted god-like powers above the normal magic available to their species in order to take over the universe.
 * Star Ocean: The Last Hope: Following World War III, three human babies were modified to survive in harsh and irriadiated enviroments, and gained magical powers in the process. The DNA used to do this was taken from a human subspecies that also had magical genetics naturally.
 * Averted in Mass Effect. Gene therapy is standard issue for soldiers and provided free for citizens by most governments, resulting in widespread perfect vision and hearing, robust immune systems, and a near elimination of genetic disorders in industrialized areas. Only modest physical enhancements are available however, with 8%-12% increases in adrenal response, clotting speed, and muscle retention etc. considered state of the art.

Web Comics

 * In the Gerosha universe, a Negative Space Wedgie called the Marlquaan is responsible for the creation of Zeran mechanics and Catacypials, the latter of which is the Alternate Company Equivalent of Pym particles. It also bonds to certain individuals directly, creating a Meta Origin database field for each of them. This allows for the Phaelites to create Phaelite Experiments' Offspring (Phexos) and their rivals the Meethlites to create Meethexos. Direct bonds are called Marlquaanites, and cannot be separated from their powers by hormone manipulation drugs like Phexos can. But as far as Muggles in southern Indiana are concerned, there is little difference between all this and straight-up magic.
 * Reasonably justified in Homestuck..

Web Original

 * Mutants in the Whateley Universe have genetic changes in a host of different genes, labeled the 'meta gene complex', and gain the ability to use some sort of extra-dimensional energy that's supposed to be the power source for the various impossible powers.

Western Animation

 * In Danny Phantom, the titular character gained his abilities to become a ghost and use ghost powers after the ghost portal mutated his DNA, combining it with "ectoplasm".
 * In Street Sharks, somehow using a formula and the blood of Genghis Khan turns a lobster and a marlin into huge evil mutant soldiers. Injecting the formula and animal DNA into a human turns them into non-evil mutants which are twice the size of their human forms, very top heavy, and able to eat virtually everything (including metal).
 * This one got to fly under Rule of Cool because the Street Sharks were totally jawsome.