Mewtwo's original name was Gigu-2 as a reference to the similar villain from Earthbound - Giegue (better known as Giygas).
Mewtwo's appearance is loosely based on Mew, with a less feline look. Its body is purple and it has three fingers on each hand. Mewtwo projects a faint purple aura when at full power.
Mewtwo has an Anime/Manga exclusive form named Armored Mewtwo in the anime, and M2 Bind in the Manga. In the anime the form increases all of Mewtwo's Psychic abilities, and in the manga it allows Giovanni to control it. Mewtwo also has another form exclusive to the Pocket Monsters manga, where it takes on the DNA of a Clefairy, becoming a shorter, fatter and much weaker version of itself.
Mewtwo is highly adept at utilizing its Psychic powers, displaying telekinesis and telepathy as well. It utilizes it's telepathy to communicate with humans and translate the Pokémon language. It is able to Fly, block special abilities, and expunge people's recollections as optically discerned in Mewtwo Strikes Back. Mewtwo when caught has a base bliss of 0 and is verbally expressed to have the most savage heart of all Pokémon
Though it technically doesn't evolve, Mewtwo has two Mega Evolutions, which appear in the Pokemon X and Y games. Mega Mewtwo Y was the first of the two to be revealed. It is exclusive to Pokémon Y Version, making its anime debut in the movie: Extremespeed Genesect: Mewtwo's Awakening. The form drastically changes Mewtwo's appearance, moving its tail to its head, giving it a long head, and changing it's eye colour, feet and hands. Mewtwo can only evolve into this form by holding the Mewtwonite Y in battle. Mega Mewtwo X, exclusive to Pokémon X Version, gains the Fighting-type upon evolution. It does not change Mewtwo's appearance as drastically, but it gives it a more "armored" look. Mewtwo can only evolve into this form by holding the Mewtwonite X Mega Stone in battle.
Mewtwo's anime debut was in Battle of the Badge! where Giovanni used it against Gary, who referred to it as an "evil" Pokémon. Mewtwo again appeared in It's Mr. Mime Time briefly. Mewtwo also appeared in Showdown at the Poké-Corral! where it escaped from Giovanni's gym, as seen in the movie. Mewtwo has been the focus of a few movies, being the main Pokémon in Mewtwo Strikes Back, in Mastermind of Mirage Pokémon under the control of Dr. Yung and Extremespeed Genesect and the Reawakening of Mewtwo. Mewtwo was also the star of the movie; Mewtwo Returns.
In the manga
It was created by Blaine in a laboratory and went on a rampage, almost destroying Cerulean City. When Red heard about "The Monster of Cerulean City", he decided to catch it. After a single encounter with the tornado that was Mewtwo, he met Blaine. Blaine told Red of his condition, how if Mewtwo continued to rampage, both Blaine and it would die. Blaine then continued to show Red his disfigured hand, a mark that he shared with Mewtwo, and concluded his talk with Red, declaring he intended to kill Mewtwo, in order to put it out of its misery, and also to save his own life. Red later encountered Blaine attempting to finish Mewtwo. Red, after stopping Blaine's attempted suicidal killing of Mewtwo, caught it using his whole team, and launching Pika with the Master Ball in its mouth, catching Mewtwo for Blaine. Blaine decided to train and raise Mewtwo as his own. Later, Mewtwo appeared alongside Blaine, battling a child helping them train. Blaine assisted Yellow from then on out, being paired with Yellow by Sabrina's Alakazam. In this setting, we learn that Mewtwo needs to rest in its Poké Ball, and if it was released for too long (over 5 minutes), it would die. It then appeared again in the FireRed and LeafGreen chapter, being loaned to Red by Blaine. It aided the Pokédex holders in stopping 9 Forretress from blowing up Neo Team Rocket's airship with Explosion, and with fighting Deoxys. Since then, it is back on Cinnabar Island, training with Blaine.
Although it is a clone of Mew, it comes before Mew in the Pokédex possibly because Mew is a Mythical Pokémon and Mythicals always come last in the PokéDex.
Mewtwo is the only Pokémon thus far to be created via cloning, although not the only one to be created scientifically: Pokémon such as Castform and the Porygon family. Genesect and the Fossil Pokémon existing in today's environment are also aided by science.
Mewtwo is the first Pokémon to receive a Mega Evolution, as well being the first Pokemon having two different Mega Evolution Forms, the second being Charizard.
Mewtwo has been noted as being the most powerful Pokémon in existence. The most recent note of this was in Mewtwo: Prologue to the Awakening, where it is stated twice.
Mewtwo is the first and only legendary to have a Mega Evolution.
Counting the original Mewtwo from the original series, along with the Best Wishes Mewtwo, and due to the events of Pokémon ranger Guardian Signs, there would be three known Mewtwo in the Pokémon world.
In all previous episodes and movies, Mewtwo's voice is heard as male, but in Pokemon: Mewtwo-Prologue to Awakening, Mewtwo's voice is female.
Mewtwo's name comes from the word 'Mew', which is like a cat meowing, and 'two' because it's a clone of Mew. It is based on a scientific cat.