From the Super Mario Wiki
The Cape is a magical yellow sheet, which is mostly used by Mario.
Super Mario series
Super Mario World
The cape first appears in Super Mario World as well as its Game Boy Advance remake. Mario and Luigi can gain it upon touching a Cape Feather (an item usually found in ? Blocks), and it gives them the ability to fly, among other things.
Super Mario Advance 4: Super Mario Bros. 3
The cape also makes an appearance in Super Mario Advance 4: Super Mario Bros 3. It could only be obtained by using an e-Reader card to scan the feather in to the player's item inventory. The feather (and in turn the cape) was also found in the Japan-only World-e level Henshin Mario de Tsukisusume!!. The cape has the same effects as it does in Super Mario World.
Super Mario World 2: Yoshi's Island
The cape appears in Super Mario World 2: Yoshi's Island and its Game Boy Advance remake, where Baby Mario could get one and become invincible by touching a star; Yoshi would turn into a Yoshi Egg and follow with the rest of the eggs.
Super Mario Adventures
In the comic series Super Mario Adventures, the cape is used multiple times by the protagonists in the story. The cape is first seen to being used by Peach who uses the cape to escape from Bowser's Castle to get away from the tormenting of the Koopalings. The cape is later used by Toad to scout out for assistance in order to help himself as well as Mario, Luigi, Yoshi, and Peach find a way back home to Peach's Castle after having defeated Bowser and his forces.
Super Smash Bros. series
The cape also appears in every Super Smash Bros. game since Super Smash Bros. Melee, where Mario uses it as an attack. It is his Side + move. While this attack is not particularly powerful, it is useful in that it can deflect certain projectile attacks. It can also make the foe spin around to face the other direction. In Super Smash Bros. for Nintendo 3DS / Wii U, the Cape can be customized to Shocking Cape, where the cape has an electrical effect and decent knockback, but it destroys projectiles instead of reflecting them. The Cape can also be customized to Gust Cape, with the cape granting a wind effect which can push opponents, but deals less damage.
Names in other languages