From the Super Mario Wiki
Super Mario series
Super Mario World
The Cape Feather is introduced in Super Mario World. As Caped Mario or Caped Luigi, the player can hover in the air, similar to the Super Leaf's effect in Super Mario Bros. 3. The flight of the Cape Feather, however, lasts as long as the player keeps hovering.
Super Mario Advance 4: Super Mario Bros. 3
Additionally, the Cape Feather is available as a secret item in Super Mario Advance 4: Super Mario Bros. 3. By scanning in the appropriate card on the e-Reader, the player can upload a Cape Feather into their inventory to use in the game. Caped Mario plays just like he does in Super Mario World, including being able to defeat enemies like Dry Bones.
Super Mario 64 DS
The Cape Feather, along with other power-ups from Super Mario World, makes a cameo appearance in the Mario Slot and Super Mario Slot minigames of Super Mario 64 DS. If the player lined up three Cape Feathers in a row, they would receive five times the number of coins they bet.
Super Mario World TV Show
The Cape Feather also appears in the Super Mario World TV show, where it is used in episodes such as "King Scoopa Koopa" and "The Night Before Cave Christmas." Mario is the only character to don the cape in the series.
Super Mario Kart
The "Feather" (as it is referred to in this game) is also found used in Super Mario Kart for the SNES as an item a driver can obtain from Item Boxes throughout the race courses. The Feather grants the user the ability to roughly perform a Spin Jump twice as high as a regular driver can. This can be useful for jumping over barriers, as a quick and easy shortcut, and for jumping over enemy projectiles.
Super Mario Maker
The Cape Feather and Caped Mario will return in Super Mario Maker, where it currently appears in the Super Mario World style.
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