Despite being Jessie's Pokémon, she doesn't really use him in battle much. Like Misty's Psyduck, he likes to pop out of his Poké Ball randomly. Jessie got it by accidentally trading her Lickitung for him with a boy named Benny.. It knows the move Counter, but it fails to perform it on many occasions. When Jessie, James and Meowth are blasting off, Wobbuffet and Mime Jr. finish by saying "Wobbuffet!" and "Miiiiiime mime mime!" Wobbuffet acts as a comic relief. Jessie left her Wobbuffet at Team Rocket HQ along with her Yanmega and Seviper when they went to the Unovaregion in the Best Wishes series.
When Jessie and James gave there pokemon to Giovanni, they had no Pokémon to use, until Wobbuffet pops up behind them, while Team Rocket gasp in suprised. Jessie retrived her Wobbuffet and heads to the Kalos region, returning in the X Y series.
It reappeared in a Pikachu short in the 15th Pokémon movie. Also, he is the third most seen Pokémon in the anime, behind Meowth and Pikachu.