Capes in Minecraft are items given to accounts related to special events and are not accessible or customizable in the base game. It is possible to download outside mods that enable capes.
Most capes belong to people who have worked on the game or who have participated in special events, such as the MineCon convention. Capes have also appeared temporarily for holidays.
Programs made by fans which modify the game, called mods for short, allow a player to alter parts of the game or access features that are not otherwise available to the player. These are available through community forums and fan websites. The official Minecraft website has some links to communities for people who make mods and other websites where mods are published. Player made mods are allowed, but not made by or supported by Minecraft, and can cause problems with the game.
Without modification, it is possible to change the appearance of the player's character by editing the skin. It is possible to draw a flat cape, but it only changes the surface and can't add new shapes that move apart from the character. For the PC game, any .png file that fits the template can be uploaded to the profile page. On XBox, skins are purchased from the XBox live store. Pocket Edition has both kinds of skin customization.