From the Super Mario Wiki
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The Bunny Hood later appears as an item in the Super Smash Bros. series, starting with Super Smash Bros. Melee. It allows the player to jump much higher and move faster than normal for a period of time. One of the Special Brawl settings in Super Smash Bros. Brawl enables players to wear a permanent bunny hood.
Super Smash Bros. Melee
Super Smash Bros. Brawl
Super Smash Bros. for Nintendo 3DS / Wii U