Mr. Game & Watch is a collection of the various characters seen in the Game & Watch games. He was never named, nor was he even a real character until he was added to the roster in Super Smash Bros. Melee.
He is, technically, the oldest Nintendo character, and has made appearances in many Game & Watch games. He is a two-dimensional, strange character who can't talk nor communicate with exception to "beeps" heard in the Game & Watch games.
In the Super Smash Bros. series
His first appearance as a character was in Super Smash Bros. Melee as the last unlockable character. He is the only character to have all his moves based off games; no moves were original or made up to suit his character. He is the only two-dimensional character and made "beep" sounds. In competitive play, he is low on the tier list, due to the fact he is one of the lightest characters in the game, his below-average moves, and his shield, which is small and only covers up some of his body.
His appearance in Super Smash Bros. Brawl looked nearly identical to his Melee appearance, but in this game, he was severely buffed, putting him in a high tier ranking. His moves are improved in both knockback and damage, his shield covers his entire body, but his weight is still very light. Despite this, he now can use Bucket to stop his momentum when hurt, saving him from K.O.s.
He is an important character in Adventure Mode: the Subspace Emissary. Not knowing the difference of good and evil, and his very low mass, the Subspace leader Tabuu decided to take him, multiply him, and have him do evil work, which includes taking Meta Knight's Halberd ship. Snake, Meta Knight, and Lucario later find them and attack. After the battle, the clones were knocked onto the deck, and turned into a large beast called Duon, a dual-ended boss character. In the end, the real Mr. Game & Watch is freed, and he joins the character roster.
His other notable appearance is in Game & Watch Gallery 4 as one of the menu characters. Although in the Super Smash Bros. games he cannot speak, he has dialogue in this. Additionally, he makes a brief cameo in the background of one of the Factory levels of Donkey Kong Country Returns.
He also makes brief cameo appearances in Rhythm Heaven Fever, where he's a character in the mini game Working Dough. He also appears in different forms depending on the mini game's theme, going from a factory worker to a chef, which are based on his sprites from the old Game and Watch Games.