Teleport Cloak

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

Examples of Teleport Cloak include:

Anime and Manga

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

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.

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.

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.