Mew

Mew is a Psychic type Pokémon. It is usually obtainable only by having it transferred to a player's cartridge at special Nintendo-sponsored events. In Pokémon Emerald and FireRed/LeafGreen, Faraway Island exists, allowing players to actually capture Mew, but access to this island requires an Old Sea Chart which is also only available through special events. Mew was the last pokemon to take a picture of on Pokemon Snap. Eventually, scientist decided to clone Mew, resulting in the powerful Mewtwo.

Super Smash Bros. Series
As of right now, Mew has been a pokeball pokemon in every game. In Super Smash Bros. he didn't do anything but was rare and lucky to see. In Super Smash Bros. Melee he dropped trophies and in Super Smash Bros. Brawl he dropped CD's. Also, in Melee, Mew's clone, Mewtwo was a playable character.