Teleport Cloak

Characters using a cloak, or a Badass Cape, for teleportation.

Anime and Manga

 * Kaede from Mahou Sensei Negima has an artifact that kind of does this... it leads to a beach house.

Comic Books

 * Cloak, of the Marvel Comics team of Cloak and Dagger.
 * Minor Marvel Universe character Devil-Slayer has a cloak that allows him to teleport.
 * Doctor Strange's cloak, sometimes.
 * The Witching Cloak in Fables.

Tabletop Games

 * An item in Dungeons and Dragons is named Cape of the Mountebank.

Video Games

 * Kirby: Meta Knight does a Mega Man-style teleport with his cape.
 * Super Smash Bros. Brawl: Meta Knight's Down Special
 * Slayer from Guilty Gear has one.
 * Runescape has several capes that teleport you, the Ardougne cape the most notable example.
 * Sort of done in Mega Man Battle Network. Bass has a cloak that he swathes himself in when he teleports, but his teleportation is an inherent ability.

Western Animation

 * Gargoyles: Odin's cloak can teleport you to a dark cold place if he's pissed off.
 * Kyd Wykkyd from Teen Titans.
 * Raven also does this a couple of times.
 * In "Dora's Christmas Carol", Dora and Swiper use "travel cloaks" to travel through time in a pastiche of A Christmas Carol.
 * El Dorado of Superfriends has this.
 * Vlad in Danny Phantom has been known to do this, though its likely more for dramatic effect instead of actually needing the cloak to teleport.
 * Mysterio of The Spectacular Spider-Man pretends to do this, but he's really combining smoke with a technology-based Invisibility Cloak.
 * Maybe Mother Gothel in Tangled, although it could just be Offscreen Teleportation.
 * Esmeralda actually did this in The Hunchback of Notre Dame, causing Frollo to think that she is using witchcraft.