Bowser's Raccoon form has only appeared in The Adventures of Super Mario Bros. 3 episode "Super Koopa". In the episode, Bowser, through the use of a powerful pendant, gained the ability to conjure and use Power-Ups, including Super Leaves.
As Raccoon Koopa, Bowser's horns and tail were replaced by raccoon ears and a raccoon tail. Using his tail, he could fly. Bowser also possibly became physically more powerful, as he was able to punch a helicopter out of the sky with his bare fist. He also combined this ability with his Fire form, which gave his raccoon ears and tail a dull gray color.
Eventually, Bowser lost his ability to turn into Raccoon Koopa after his pendant overloaded and exploded, due to using too many transformations in a row.
This form appears again in Super Smash Bros. for Nintendo 3DS / Wii U, via Bowser using a Super Leaf. Unlike the TV episode, however, the raccoon ears and tail are added to his appearance, rather than replacing his horns and tail. Like the other fighters, he only gains the ability to glide in this form.