Cape Wings

Some characters - often of the Badass variety - have a mysterious way of controlling even the very fabric of ~~reality~~ their clothing. They can turn their cape (generally a single piece of cloth) into a pair of fully functional wings (generally not a single piece of cloth), and then back again without any damage.

Probably because they look cooler, these wings often appear demonic or bat-like.

It might not always be clear if the wings turn into a cape or the cape turns into wings. It's best not to think about it.

Some examples take this even further, making the cape a form of Morph Weapon, capable of turning into many different things. Compare Prehensile Hair.

Examples of Cape Wings include:

Anime and Manga

Laharl in Makai Senki Disgaea, even though what he's wearing is actually a scarf.
A one-shot villain from The Law of Ueki had the power to turn his cape into feathery wings, and could also use the feathers as projectiles.
There's a vampiric variant in Vampire Hunter D: Bloodlust. Meier Link can turn his cape into bat-like wings, and his hands into armored claws.
Sidoh the Shinigami from Death Note.
Evangeline of Mahou Sensei Negima. Her cloak can also turn into a swarm of bats.
- Since the cloak usually seems to start out in bat form, it's probably the other way around.
Science Ninja Team Gatchaman (aka G-Force, Eagle Riders) are an example. Come to think of it Zoltar's cape behaved interestingly from time to time too....
Both G Gundam‍'‍s Master Gundam and Gundam Wing‍'‍s Deathscythe Hell have mechanical wings that transform into a cloak that covers their body; the movie version of Deathscythe takes it a step further by having the wings be lined with thrusters for exceptional mobility.
In another Humongous Mecha example, some incarnations of Getter Robo have this power. Unlike the above example there is usually no plausible mechanism for this, much like everything else about Getter Robo.
Berserk: Femto (a.k.a. Griffith) looks a lot like a blood-red demonic version of Batman, with his evil-looking hawk-hood and his dark and menacing batlike Cape Wings.
Zeon of Gash Bell has a cloak that responds to his will, expanding wildly to attack and defend as needed. Gash later inherits it after Zeon's Heel Face Turn.
The title Humongous Mecha of Vision of Escaflowne is able to transform into a dragon. Its cape forms the fabric of the wings.
Dukemon/Gallantmon of Digimon Tamers when he mode-change into crimson mode.

Comic Books

Linda Danvers/Matrix version of Supergirl. She becomes an earth-born angel, and her cape can turn into flaming wings.
The cover art to Superman #659 (link) depicts Superman floating above a crowd, with a pair of red angelic (though still vaguely cloth-like) wings instead of a cape. The story is about an old woman who is convinced Superman is an angel.
In PS238 during a trans-dimensional jaunt, Cecil Holmes had his trenchcoat made "living" and capable of forming wings by the forces of Chaos (a.k.a. his classmate's mother). It becomes permanent. Naturally, his reaction upon experimentally confirming that this works in the mortal world was overexcited:

I'm so never taking this coat off again! Not even to shower!

Film

In Final Fantasy VII: Advent Children, Vincent's cape is something like this: it sort of flows.
Batman Begins and The Dark Knight did this with Batman's cape. Justified in that the wings were only for gliding, with "memory cloth" in the cape going rigid when you apply an electrical current.
- And before that, it was done in Batman Returns.

Literature

As Discworld vampires follow mostly cinematic tradition, some of them (particularly Arthur Winkins, the Count Notfaroutoe and a full time vegetable merchant), need the cape to transform into a bat.
In The Krytos Trap, part of the outfit Wedge Antilles wears while trying to talk some Twi'leks around, along with Fingerless Gloves and a Loin Cloth, is a cape cut in such a way that it fell in two red wings.

Tabletop games

Warhammer has a non-batlike version in the lizardman item Cloak of feathers.
Dungeons & Dragons has several versions of magic cloaks that can turn into wings. Usually these are of limited usage, about an hour a day, useless for long distance flight.

Video Games

Meta Knight in the Kirby games and Super Smash Bros. (as seen in the picture above) but not in the anime, where he only had wings in the pilot.
- Averted in Return to Dreamland. In the opening cutscene, Meta Knight removes his cape, revealing a small pair of wings under it.
- In Super Smash Bros Brawl's Subspace Emissary mode, he gets shot with a laser in the wing, which starts to burn off that wing. He lands and transforms it into a cape, which stops the burning and heals the damage somehow.
Roc's Cape in The Legend of Zelda Oracle Games, The Legend of Zelda Four Swords, and The Legend of Zelda the Minish Cap.
Dante in Devil May Cry 3 does this with his coat.
In Boktai 2: Solar Boy Django, While in Vampire mode, Django's scarf turns into (or at least takes the shape of) a pair of wings. I'm not sure if he uses them to fly or if he just uses generic "vampire levitation" powers during his attack when he flies across the screen.
In Castlevania: Symphony of the Night, Alucard's longcoat momentarily turns into a pair of bat wings when he double-jumps, and his wings in bat form are the same color as his cape.
- Soma Cruz of the Aria subseries also appears to turn his ~~longcoat~~ pimp coat into the wings of his bat form.
- Dracula also sometimes turn his cloak to wings, in Curse of Darkness and Dracula X Chronicle.
Morrigan's wings in Darkstalkers can transform into a swarm of bats, become blades, spikes, or tentacles, or clothes in her win poses.
In Okami, Waka's Cool Hat has long wing-like extensions which are apparently functional.
Legacy of Kain plays with this; Raziel's actual bat-like wings are broken and the tattered shreds hang behind him like a cape, but he can still use them to glide for short distances.
Laharl's scarf can turn into wings though this is only shown in the anime. Even then, he's not that agile a flyer. Also, most nosferatu/vampires.
Batman: Arkham Asylum and Batman: Arkham City use the same "memory cloth" justification as in Batman Begins to enable Batman to glide like his namesake.

Web Comics

Ariel from Drowtales explicitly does it with magic for a one-time stunt. Hilarity Ensues when said stunt gets derailed by Liriel.
Mink from Darken can do this.

Web Original

The dating website Soul Geek has different pieces of mini-fiction, along with iconic characters, used in the advertising. One of the pair of vampires is showing with a cloak that rises up on one side in a huge wing.
Oblivion from Shadowhunter Peril is shown to do this when he gets pissed. It generally preludes his transformation into an Eldritch Abomination. Once he completes his transformation, he keeps the wings, but now they're FLAMING.

Western Animation

The Gargoyles can fold their wings up into capes when not using them.
- Greg Weisman at least admitted this was physically impossible by any stretch of the imagination.
Megatron in Beast Machines, via transformation. The red dragon wings invert and become his blue cloak, which he uses to hide the fact that he still hasn't purged himself of his dragon form.
Big Chill has a pair of wings that form a makeshift cloak when out of use.
In Avatar: The Last Airbender, Aang uses his short cape and Blow You Away to jump higher. Way higher.