The Bunny Hood debuted in The Legend of Zelda: Ocarina of Time as a collectible mask. One of the side missions in the game required Young Link to sell various masks to the citizens of Hyrule. Young Link found the Running Man in Hyrule Field and sold the Bunny Hood to him. In exchange, the running man paid him the maximum amount of Rupees that Young Link's wallet could hold. Once Young Link sold the Bunny Hood, he was able to borrow it from the Happy Mask Salesman at anytime. The Bunny Hood returns as a collectible mask in The Legend of Zelda: Majora's Mask. In this game, Young Link can collect the Bunny Hood from Grog. When wearing the Bunny Hood in this game, Young Link's speed and jumping distance increases, whereas it had no effect in Ocarina of Time. 
As an item
The Bunny Hood appears as an item in Super Smash Bros. Melee. Once picked up, a character will become quicker and can jump much higher. It will also work on Jigglypuff and Kirby's additional jumps. Furthermore, the hood increases the character's movement speed and falling speed. The effect lasts about twelve seconds. It can fall off of a character if they are hit hard enough. The Bunny Hood also appears as a collectible trophy.
This trophy is unlocked by getting 125 combined combos with all characters in Training Mode.
Don the Bunny Hood to improve your agility drastically, allowing you to jump great distances and move at high speed. The ears are a cute accessory: they're even adorable on characters they don't quite suit. The Bunny Hood was key in Majora's Mask, where it made Link move at one-and-a-half times his normal speed.
As an item
The Bunny Hood returns in Super Smash Bros. Brawl with similar effects from the previous game. In addition, a "Bunny Brawl" option exists in Special Brawl mode, which gives every character a permanent Bunny Hood, which cannot be knocked off. The Bunny Hood appears as a collectible trophy in Brawl.
Headgear that hugely improves your jump and movement abilities. True to its name, the hood comes with a pair of cute, fuzzy ears. On the right characters, they're as cute as can be, but on the wrong ones, they're...scary. Of course, that adds to the item's charm. The sudden speed increase you get is responsible for more than a few self-destructs, so be careful.
As an item
The Bunny Hood returns in Super Smash Bros. 4. It is almost exactly the same as in Brawl.
In Smash Tour
The Bunny Hood is one of the items that can be found in Smash Tour, giving the user the ability to start a battle wearing a Bunny Hood.
This hood is beloved by a man with a passion for nature who longed to emulate a long-lost breed of bunny. Wearing this hood, he gained impressive leg power that allowed him to run for days on end. If you don this hood, you'll leave your foes in the dust with enhanced speed and jump power.
A hood beloved by a man who longed to be...a bunny. It gave him unrivaled leg strength, allowing him to run at top speed all day and night. In this game, it boosts your speed and jumping ability, so you can get behind enemies easily and recover quickly if anyone launched you!
As an item
The Bunny Hood returns once again in Super Smash Bros. Ultimate, acting the same as in Smash 4.
Equipping the Postman, Cereza or Jelfonzo Support Spirits will give the player a Bunny Hood at a start of a match.