Unstable Genetic Code

""The Haggunenons of Vicissitus Three have the most impatient chromosomes of any life form in the Galaxy. Whereas most races are content to evolve slowly and carefully over thousands of generations, discarding a prehensile toe here, nervously hazarding another nostril there, the Haggunenons would do for Charles Darwin what a squadron of Arcturan stunt apples would have done for Sir Isaac Newton. Their genetic structure, based on the quadruple sterated octohelix, is so chronically unstable that, far from passing their basic shape onto their children, they will quite frequently evolve several times over lunch.""

- The Hitchhiker's Guide to the Galaxy

A creature exhibits power to change shape, unpredictably and often uncontrollably. When shapeshifting isn't exotic enough to explain this, Hollywood Evolution might do just fine. Suggest that the creature has an Unstable Genetic Code, and it can "evolve" without regard to Evolutionary Levels.

Of course, this is nonsense in Real Life.

Anime and Manga

 * Pokémon
 * Eevee is said to possess this in its Pokedex entry. It has 7 different evolved forms, each of different types... and counting (we started with only 3)! The Pokémon Special manga takes it a bit further. In it, there's a Eevee that was specifically tested on by Team Rocket, as a beta test to attempting to merge the legendary birds. Eventually it comes into the hands of Red, who helped it overcome its past. From that point on, it gained the ability to evolve and devolve freely between Eevee, Flareon, Jolteon, and Vaporeon. Red even had the three elemental stones with him at all times.
 * Ditto's DNA is also said to have an unstable, but regularly malleable. This is apparently what lets it shape itself into any other Pokemon, and breed with any Pokemon capable of it.
 * In Bio-Meat: Nectar: Nectar, the USBM's reproductive and ambulatory abilities (which it was never designed to have) are all explained with this trope.
 * in Majin Tantei Nougami Neuro.

Comic Books

 * The Deviants, and therefore, the Skrulls, in the Marvel Universe were originally this.
 * This was the explanation used for Toad's initial pathetic Quasimodo-like appearance and "abilities". When it was corrected, he suddenly Took a Level in Badass and turned into a sleek, cocky and dangerous acrobat molded in the likeness of Ray Park.

Film
"Red Queen: One of the Hive's early experiments, produced by injecting the T-virus directly into living tissue. The results were unstable. Now that it has fed on fresh DNA, it will mutate - becoming a stronger, faster hunter."
 * In the Resident Evil movie, the protagonists see a horrifying monster eating a dead body:

Live Action TV

 * Doctor Who episode "The Lazarus Experiment". A scientist alters his own DNA to become young again but it becomes unstable, causing him to start changing from a human into a monster and back again.
 * More than thirty years earlier, Doctor Who did something similar in "Planet of Evil," but the scientist was infected with anti-matter. Which is even sillier.
 * The '90s Outer Limits had an episode where the high-school teacher activated the introns in his DNA. This resulted in a map growing on his back, which he is intended to follow.

Newspaper Comics

 * In Safe Havens, Samantha has messed with her DNA so many times it's now unstable, causing her to randomly change at inopportune times.

Radio

 * The Hitchhiker's Guide to the Galaxy radio show described the Haggunenons this way. (They didn't appear in the books, which replaced the Haggunenon subplot with one involving Disaster Area.)

Tabletop RPG

 * Dungeons & Dragons 3E has both Chaos Beasts from the "Monster Manual", and the Hagunemnons (yes, a HG2G reference) from the "Epic Level Handbook". Both of them have no real form, but constantly morph between countless shapes.
 * In Warhammer40000, various planets - especially Death Worlds - tend to have monstrous creatures as one-offs and adaptive mutations. Subverted at times when it's actually Chaos magic mutating them; played straight at other times, ESPECIALLY with the Tyranids.

Video Games

 * "Hazmat" in Marvel Nemesis: Rise of the Imperfects. He has unstable DNA (a "living mutation") due to injections of untested immunization vaccines.
 * After being fatally shot, in Resident Evil 2 injects himself with a siringe that contains the G-virus, which at first causes his wound to heal almost instantly. But it doesn't stop there.
 * The point of the  in the first Parasite Eve game. It would be able to take over the world as it could change its DNA at will to overcome any resistance.

Western Animation

 * Danielle "Dani" Phantom, a female clone of Danny Phantom, has unstable DNA that causes her to melt into ectoplasm whenever she turns into a ghost and uses her powers. But she got better.
 * Beast Boy from Teen Titans is stated to have this.

Real Life

 * While not quite as extreme as some of the examples above, in-generation changes in an organism's genetic code through horizontal gene transfer is commonplace among bacteria and archaea, and not unheard of in eukaryotes.
 * Plants sometimes express mutations in one portion of their anatomy, such as a single root or branch, that make that part visibly different from its parent stalk. Such mutations can actually prove valuable, as with the 'golden delicious' strain of apple, which was derived from a single mutant branch of another strain of apple tree.