Mix-and-Match Man

This is an Artificial Human, usually but not always a clone, who is created from the combined DNA of multiple individuals. Sometimes the intent was to clone a single individual exactly, but extra genetic samples were added to the mix by accident. Other times, this is done on purpose to give the clone specific traits from each genetic donor.

Non-clone Mix And-Match Men are physically built from parts of other people, literally stitched together.

Can be Half Human Hybrids when at least one genetic donor is human and at least one isn't. Can be Mix-and-Match Critters when all genetic donors are non-humans, such as Human Aliens. Obviously more likely to occur in settings where Designer Babies are common. Lego Genetics are a prerequisite for making these out of vastly different species. Patchwork Kids is when an individual produced by normal reproduction might as well be one of these.

Anime & Manga

 * Cell from Dragon Ball Z. As the name suggests, he was created from the DNA of the strongest fighters in the universe.
 * Giorno Giovanna from Jo Jos Bizarre Adventure. While he's not a clone of anyone in particular, the strange circumstances around his conception gave him characteristics of both Jonathan Joestar and Dio Brando. This is reflected in his name: JoJo + Dio = GioGio . Turns out there's three other men created from these same circumstances, they appear in Part 6.
 * Tenchi Muyo!'s Ryoko was made by.
 * In Appleseed, the Bioroids were created with DNA from several donors, including the father of heroine Deunan.
 * Rei is formed from the DNA of.

Comics

 * The current version of Superboy from the Superman comics is a combination of Superman and his arch-nemesis Lex Luthor.
 * Deadpool probably counts, but he was a normal human before the Mix-and-Match.
 * Damage is somewhere between this trope and Designer Babies; his genes were taken from all the original Justice Society of America.
 * The Silver Age DC Comics hero Ultra, The Multi-Alien was a man (in the future) who was a victim of four alien criminals trying to create a means to replicate armies of themselves to conquer the universe. He ended up with a freaky composite body and each of the aliens' powers, which he then used to become a superhero. (He later finds a way to switch back-and-forth between human and multi-form.)
 * Brianna from Fred Perry's Gold Digger was created with the traits and memories of her two "sisters" in a Freak Lab Accident.
 * DC's Composite Superman. Depending which version you're talking about, he has the combined powers of Supes/Bats plus some JLA folks, or the combined powers of a buttload of Legion of Super-Heroes members.
 * Amazo is an android who copies any superpower he is exposed to.

Film

 * Arnold Schwarzenegger and Danny DeVito's characters from Twins.
 * The version of Deadpool used in X-Men Origins: Wolverine fits the trope even more so than his comics counterpart, having Wolverine's regeneration, adamantium skeleton, and adamantium katanas protruding from each wrist, in addition to Cyclops' eye-beams, Kestrel's teleportation, and his own superhuman hand-eye-coordination.
 * Sid 6.7 from Virtuosity is sort of like this - he was a computer program created from the personalities of 183 criminals (and an orchestra director), which tricked a programmer into placing him in an android body so he could do damage in the real world.
 * Mel Brooks Young Frankenstein: like the original Frankenstein's Monster, he's built of parts from corpses.
 * The protagonist of Cronenberg's The Fly kidnapped his pregnant love interest in an attempt to merge himself, her, and their unborn child into this trope. It's unclear if this could possibly have worked, but at the time he was so desperate to suppress his transformation into a human/fly hybrid that he wasn't thinking straight.
 * In The Fly II, that child has grown up, and
 * "Lazarus" from the 1995 Sy Fy Channel Movie Mr. Stitch is a sort of Frankenstein Monster made from the corpses of eighty-eight people of every race, age and lifestyle, split evenly among gender and given an identity of his own. Things go wrong when it turns out he has Genetic Memory.
 * The reason why the title villain in Monster Man is killing and amputating people is because he needs bodyparts to patch up his resurrected brother.

Literature

 * In Animorphs, Ax's human form is one of these. He took DNA from four of the other Animorphs to create his human form, so he wouldn't look like a copy of anybody.
 * Specifically, two boys and two girls, creating a result that is regularly described as "disturbingly pretty".
 * The Replica series of novels has one of these as the main character, created deliberately to be an Ubermensch.
 * The title character of Robert A. Heinlein's Friday.
 * Same author, the character of Minerva in Time Enough for Love.
 * Also Minerva's twin sister, Pallas Athena, who finally gets a body with the exact same DNA as Minerva in Heinlein's novel To Sail Beyond the Sunset.
 * Frankenstein's monster is made up of various spare parts.
 * Or at least Hollywood has made him as such - the novel gives almost no details about it. The Dean Koontz version, however, goes so far as to identify what sort of people his parts came from.
 * Darci, the protagonist of the sci fi novel Star Split, is eventually revealed to be a chimera, or someone made of multiple strands of DNA. This itself isn't unusual in the far future world where genetic engineering is the norm, but she's a special case.
 * Damsel in Soon I Will Be Invincible.
 * In Donald Moffitt's Genesis series, all humans created by the Nar use this as their preferred reproductive method, as the human gene pool is still too limited to allow random breeding.
 * Flinx from Alan Dean Foster's Humanx series was conceived via this trope by criminal scientists, who spliced together DNA from dozens of psychically-inclined sources.
 * The Igors on Discworld typically have parts from multiple people, and can replace someone else's missing parts as well. (There is also, in one book, a mention of a Mix-and-Match Horse.)
 * Invoked from an alien POV in Perdido Street Station, when an insect-headed khepri describes humans as "khepri bodies with the heads of shaved apes".

Live Action TV

 * Adam from Season 4 of Buffy the Vampire Slayer was an amalgam of most of the monsters that the Initiative had captured and was taken out by and amalgam of the main characters.
 * Tuvix in the Star Trek: Voyager episode of that name--a blend of Neelix and Tuvok, created by a transporter accident.
 * Luke Smith in The Sarah Jane Adventures.
 * Doctor Who: The Doctor clone with some of Donna's DNA.
 * Morbius's second body, being a tribute to Frankenstein's monster.
 * Max from Dark Angel.
 * It's implied that Mr. Spock was conceived in this way. The Expanded Universe novels outright say he was, but as always, there are Canon issues with those.
 * Star Trek: Enterprise had baby Elizabeth, created from human and Vulcan DNA with a fatal flaw deliberately introduced by a hate group to make her a Straw Loser of a particularly heartbreaking kind.
 * House had a patient like this. A boy had a few groups of cells throughout his body that were the result of two fertalized eggs fusing together immediately after fusing to the uterine wall.

Tabletop Games

 * In Promethean: The Created, all Frankensteins are made from pieces of at least two separate corpses. It's in the name - the first one was that Frankenstein's Monster. Theoretically, any Promethean can be a mix-and-match, but a Frankenstein has to be.
 * Magic: The Gathering has Goblin Chirurgeon, whose art depicts one of his patients. Also from Magic we get the Phyrexians, who do this...and a bunch of other Body Horror. Phyrexian Rebirth turns all creatures in play into this.
 * Innistrad uses this as the distinction between black zombies, which apply the rotting-reanimated-corpse model, and blue zombies, which are the product of blasphemous experimentation rather than blasphemous rituals.

Video Games

 * Agent 47 from Hitman (Chinese, German, Romanian, Russian and South American fathers).
 * Liquid and Solid Snake being twins, are confirmed to be part-American, part-Japanese and part-Chinese (or whatever the hell Eva is).
 * Emerl from Sonic Battle is designed to combine the movesets and personalities of the people he meets. When the only people he's met are Sonic and Tails, others can't tell if he's being rude or polite.
 * A non-genetic example is Ermac from Mortal Kombat, who is made up of the souls of hundreds of dead warriors bound into a humanoid body.

Webcomics

 * Drowtales: Rik the half dragon is something of a genetic experiment, and is ostracized by a society as a result.
 * Grace from El Goonish Shive is human and also part squirrel, with alien DNA from an Uryuom and a Lespuko (sort of like an Uryuom, long story).
 * Unity of Skin Horse is sewn together Frankenstein-style from mismatched parts.
 * As is Quilt from Dominic Deegan.
 * Baron Wulfenbach form Girl Genius is probably one of these. The family originally had three sons, but following a horrific lab accident two of them disappeared. It's commonly believed that the Baron is a construct made of the salvageable parts of all three. Also, Constructs in general.
 * Homestuck:.
 * Molly in The Inexplicable Adventures of Bob was grown using genetic material from many different animals--and some human DNA, taken from her "mother," Jean Poule.

Western Animation

 * Romy from Pinky and The Brain was supposed to be a normal clone of Brain, but DNA from Pinky was accidentally included in his creation, causing him to inherit traits from both mice.
 * Serpentor from G.I. Joe was created from the combined DNA of ten historical figures: Julius Caesar, Napoleon Bonaparte, Attila the Hun, Philip II of Macedon and his son Alexander the Great, Ivan the Terrible, Vlad the Impaler, Hannibal, Genghis Khan, and Grigori Rasputin. Dr. Mindbender tried to get Sun Tzu as well, but was stopped by the Joes. Fortunately, that was apparently enough to throw his military competence out of whack.
 * Delilah from Gargoyles is a combination of Elisa Maza and Demona.
 * The TMNT 2k3 incarnation of the Rat King (a.k.a. "The Slayer") is one of these, using DNA from Bishop, Splinter, among other possible sources.
 * This happens in The Secret Saturdays when Zak and his pet komodo dragon and gorilla-cat are combined into one being.
 * Robot Chicken brings us the horror of Composite Santa: genetically/visually one-half Santa, one-half Frosty the Snowman. I don't know what his powers are, but he freaks me right the fuck out.

Real Life

 * Chimera of this type can occur naturally when two embryo fuse in the womb. One case resulted in a woman whose apparent genome did not match her childrens' because her salivary glands and ovaries actually had two different genotypes.
 * Actually everyone has a slightly different version of Chimeraism occurring from cellular interchanges during pregnancy. Babies pick up a few from mom and mom from the child. However, these are very few.
 * In addition to sexual reproduction blending the DNA of two individuals, much of our DNA is in fact viral in origin. These viruses began somewhere else, often in another species.
 * Cloned animals are typically a Mix And Match of two parents: the animal from which they are cloned (which provides the nucleus of the lab-generated zygote), and the animal that provided an unfertilized egg (which provides the other cellular components). They have the chromosomes of their cloned parent, and the mitochondrial DNA -- what little of it there is -- of the egg-donor. Averted if the same female animal is used for both.