Mewtwo (ミュウツー, Myūtsū) is a fictional creature from the phenomenally popular and expansive Pokémon media empire. It was introduced as the "final Pokémon" in the very first game in the franchise. Mewtwo enjoys a good degree of fame and popularity in the Pokémon fan community for being a far more human-like character than most other Pokémon, and it was included in Super Smash Bros. Melee as a playable character. It was one of the five characters to not return as playable in Super Smash Bros. Brawl however.
 Character description
Mewtwo is Pokémon #150 in the Generation I Pokédex, the final Pokémon in the list not counting the generally-unobtainable Mew which is #151 in the Pokédex. It is a clone of Mew that has been altered by unscrupulous scientists in order to increase its power and ruthlessness in battle. As a result, it is visually similar to Mew: a pale purple, vaguely feline humanoid with strong psychic powers. Unlike Mew, Mewtwo has the height and mass of an adult human, and thinks of nothing but fighting and defeating its opponents.
In-game, Mewtwo was designed to be the "final" Pokémon of the Generation I games, having a immense Special stat, the highest base stat total with a total of 590, and the (at the time clearly overpowered) Psychic type. As a result Mewtwo was an overcentralizing force that unbalanced the metagame until the next generation's Special split into Special Attack and Special Defense, and altered type interactions evened the playing field.
In the Pokémon anime and movie series, Mewtwo is a one-of-a-kind Pokémon that develops a hatred for humans and the concept of subserviant Pokémon, attempting to prove the superiority of clones over originals. It later has a change of heart and becomes a sort of anti-hero, mostly keeping to itself and trying to find its purpose.
 In Super Smash Bros.
According to a page on the Japanese Super Smash Bros. site, Mewtwo was planned to be playable, but was cut; Bowser and King Dedede are also mentioned as having been cut, though no other information is available. 
 In Super Smash Bros. Melee
 As a playable character
Mewtwo made its Smash-series debut as an unlockable character in Melee. It is much more difficult to unlock than most other secret characters in Melee, however; it can be unlocked after either playing 20 cumulative hours of Vs. Mode matches (5 hours for four players), or playing 700 Vs. Mode matches.
Mewtwo's playstyle is very floaty and includes a decent variety of combos, strong throws, a very good wavedash, above-average dodges, strong projectile, and exceptional recovery. On the other hand it has a bad combination of large size and light weight, with its floatiness resulting in being an easy combo target, in addition to lacking solid KO options and having slow movement speed. As a result Mewtwo has sat in the bottommost part of Melee's tier list for most of the game's lifespan, and only recently has climbed its way to its current position of 21st.
Mewtwo, as a playable character, has three trophies - a main trophy acquired by defeating the Classic mode with Mewtwo on any difficulty, and the two Smash trophies are by beating the Adventure and All-Star modes, respectively. Its Classic mode trophy reads:
Mewtwo appears in Brawl as a collectible trophy, obtained by completing All-Star Mode on Intense difficulty. The trophy describes Mewtwo's appearance in the Pokémon games, and makes no reference whatsoever to its appearance in Melee:
 Unfinished data
While Mewtwo does not appear as a playable character in Brawl, data of the character has been uncovered through hacking, as ef_mewtwo.pac. The exact reason why the data is included is unknown; it is theorised that Mewtwo was scrapped in development, or the data was simply imported from Melee for referential purposes.
Of note however is that the data for Mewtwo has its own unused fanfare, as "snd_bgm_Z38_MYU2". Many other claims have been made about the progress of Mewtwo's data, such as an included character model and even parts of its voice, though these claims remain unverified. To date Mewtwo has had the most claimed unused content of any scrapped character.
 In Super Smash Bros. 4
During the Pokémon X and Y Developer Roundtable at E3 2013, a question was asked of the developers whether they would like to see Mega Mewtwo appear in the next Smash Bros.. While the developers were unsure what to answer and replied with a generic lack of comment, Sakurai happened to be in the audience, and was claimed to exclaim "We are thinking about it.". While neither Mewtwo nor Mega Mewtwo have yet been confirmed or denied for SSB4, this statement combined with Mewtwo's recent popularity in the Pokémon series brings many fans to believe a comeback is more likely than not.