Cape

Capes (previously known as cloaks) are extremely rare vanity items and are worn in addition to the player's skin. They are closely related to elytra which they visually modify.

Obtaining
There is currently no way to obtain a cape on one's own on, although there are various mods that allow players to obtain one, only visible to that player (or in some cases, other users of that mod).

$$ of the game, some skins from various skin packs include capes.

Players on who legitimately have one or more capes can choose which to wear (including no cape) by going to their Minecraft profile.

Players on can equip or unequip certain capes for their skin via the Character Creator.

Unused Capes
Minecon 2011

These capes were featured in a poll where MINECON 2011 attendees could vote for their cape of choice. The red creeper cape won MINECON 2011, and the blue cape with the pickaxe was for MINECON 2012. These following capes are still unused though may appear in the future.

Bedrock Edition Skin Pack Capes

These capes are from Bedrock edition skin packs and are currently not used in any skin pack.

Elytra
When a player has a cape and equips an elytra, the elytra wings take the place of the cape and adopts its custom design.