In Super Smash Bros. Melee and its successor, Super Smash Bros. Brawl, Wobbuffet appeared as a Pokéball Pokémon. In the games, Wobbuffet would use the move Counter to attack players. It would rock back and fourth and do so more violently if the player attacked it or threw an item at it. When the player touches Wobbuffet before attacking it, it'll still cause knockback, though the player won't take any damage.
Interestingly, Wobbuffet is the only Pokémon not classified as Legendary to appear in the event Legendary Pokémon in Melee. Some have speculated as to why this is. One opinion is that it surprises players to expect to find a Legendary Pokémon. Another is that Wobbuffet can prove quite useful, so while it doesn't make since why he appears, it's appreciated nonetheless. It should also be noted that Smogon, a popular Pokémon website, classifies Wobbuffet as an "uber", or as one of the most powerful Pokémon in the game. It and its pre-evolution form are the only ubers in the series.
Super Smash Bros. Melee
"A Patient Pokémon, Wobbuffet lives in darkness to hide its mismatched black tail. Even for a stoic Pokémon, this creature is a testament to self-control; it will not actively attack an opponent. Its Counter and Mirror Coat moves are solely used for reflecting attacks directly back at its antagonist"
Super Smash Bros. Brawl
"A Patient Pokémon. A nocturnal, cave-dwelling creature, Wobbuffet is calm and collected, but it will fight back viciously if its black tail is attacked--this hints at something secretive about its tail. If Wobbuffet is put into battle, the opponent cannot run away or switch. Females have lipsticklike markings around their mouths."