Bandaged Face

Basically, wearing bandages on the face. The whole face, and (generally) nothing but the face. Usually they're worn because the character's undergone some sort of facial surgery or they are very badly disfigured, though occasionally there are other reasons, such as the desire to keep one's identity a secret.

Covering one's face in bandages serves two purposes:

For better suspense when they are unwrapped during a Dramatic Unmask, or
As a creepy (and kinda cool) way of disguising yourself.

Compare Bandage Mummy, for when the complete body is wrapped for comedic (or dramatic) purposes, and Bandage Babe, where bandages are Fetish Fuel. Contrast Pointless Band-Aid, where only one bandage is worn on the face.

Examples of Bandaged Face include:

Anime and Manga

Unit 01 from Neon Genesis Evangelion after losing the head armor disguising her organic nature.
Schwarzwald from The Big O, though the reason is unclear. It's suggested that he burnt himself by tripping off security features while attempting to activate Big Duo, but it's never outright stated.
Onigumo(?) from Inuyasha after an accident is seen with his face bandaged this way as he's cared for in a cave by Kikyou.
Habashira Rui from Eyeshield 21 wraps his entire body in bandages so he wouldn't be noticed when he tries out for Team Japan to go to the World Cup. Dramatic Reveal comes several chapters later.
Detective Conan: A murder happens aboard a boat with a costume/masquerade party, where some characters are dressed as mummies. Also, the detective who solves the murder, thought to be Shinichi but actually Heiji in disguise, is dressed up as The Invisible Man.
- Another Detective Conan example - the fact that a man wore a full face bandage was used to create alibis for the real murders--they disguised themselves as him after he committed suicide.
The first book of The Kindaichi Case Files featured a girl in flashbacks who had to do this due to severe burn scars she suffered when acid was spilled on her face. Later, the killer of the book does the same thing to hide his identity while getting himself set up to commit his murders.
Shishio 'Mummy' Makoto of Rurouni Kenshin has the burns-all-over kind. Doesn't generally bother wearing any clothes, he's so thoroughly bandaged. There are just eyes staring out. He even has a nice little...bandage-hat...thing...with bandages that hang down kind of like hair. Which should probably have been a clue that he had a metal helmet so he couldn't be shot in the head again, rather than just being bandaged on the skull.
Mukuro from Yu Yu Hakusho is an immensely powerful, short, rough-spoken demon lord swathed entirely in bandages who recruits Hiei after the Chapter Black arc is over. Turns out they're covering two things: she's female, and half of her is an acid-burned hideous wreck.
- But they make such a cute couple!
- "Happy Birthday."
- Genkai
From Soul Eater: Crosses over with Scarf of Asskicking for Kishin Asura as his deranged method of protecting himself from others. These 'bandages' are made of his own skin.
- There's also Sid's partner, Nygus.
Black Butler: In the manga Baron Kelvin has this once he gets surgery to make himself look more beautiful.
This is one of the depictions of Lucy from Elfen Lied.
Naze Youka from Medaka Box covers her face in bandages not only to hide her good looks, but to keep her true identity under wraps, as it were.
Heinkel ends up with one at the end of Hellsing. They're mostly for rule of cool, considering they billow around her head, and aren't remotely wrapped around her Glasgow Smile.
Eureka have bandages over a portion of her face for a brief moment in Eureka Seven movie due to the sun's effects.
The cover image^{[dead link]} for Lupin III : Green VS Red, itself a nod to The Castleof Cagliostro.
Played for laughs in Ranma ½ when Ranma bandages his entire face in order to hide his expression and to also hide cards that he can cheat with in poker.
In "Mirai Nikki", Fourth ends up like this after Yuno shoots his ear off.
At one point in Berserk, Casca has her face bandaged up in order to hid her face from men who want to have their way with her. Another So Beautiful It's a Curse scenario.
Older Than They Think: Kei from Akira also did this to hide her gender from possible rapists after Akira loses control of his powers and obliterates Neo-Tokyo.
Happens to Inui in The Prince of Tennis, after a rather bloody doubles match. Caused lots of immature giggling in the fandom.

Comic Books

Pictured, the second incarnation of The Unknown Soldier from DC Comics, though both follow this trope.
Hush, from the Batman comic, also covers his face in bandages.
The Negative Man and Negative Woman in the DC Universe. Both have to wear those special bandages to contain the intense radiation their bodies emit that is part of their energy being powers.
Harvey Dent, aka Two-Face from Batman, has this happen in his first appearance after he is scarred by acid—complete with dramatic unwrapping to reveal the scar tissue. This happens subsequently every time he goes in for facial reconstruction surgery (like in The Dark Knight Returns).
The Red Skull had a Bandaged Man around him for a while, who was told to be Doctor Doom, then deciding that having Doom be in World War Two was silly so it was Retconned into him timetravelling. He also didn't kill Adolf Hitler because his original death at the hands of the original Human Torch was "fitting" but that's neither here or there.

Film

The Hungarian survivor on The Usual Suspects.
Owen Wilson's character in "The Darjeeling Limited"
Several James Bond movies, including Thunderball.
This is used with Willem Dafoe's character in Once Upon a Time in Mexico for reasons of plastic surgery.
The Joker in the 1989 Batman film.
Darkman
The antagonist from Timecrimes.
Castor, briefly, in Face Off.
Dark Passage
Two men in Force 10 From Navarrone, allegedly due to flamethrower burns. They actually had never been injured at all.
In Mr Stitch, the patchwork man Lazarus spends the first part of the movie with a bandaged face - and everything else - as his many, many, many sutures heal.
Michael Myers at the beginning of Halloween 4.
The killer in the Hong Kong slasher The Deadly Camp.
Keller from Freak.

Literature

The Invisible Man is the Ur Example of a specific type of this: wearing bandages on the face not because of an injury or due to being a mummy, but as a way of hiding one's self.
- Or, in this case, one's lack of a self.
Vaguely-remembered example, possibly an abridged version of a longer story: A wealthy Southern man is traveling north with his slave. The rich guy is sickly and always has to wear bandages on his face, possibly because of burns. In the end, when the pair arrive at their destination, the slave owner takes off his bandages and reveals "he" is actually a woman, and also a slave, and both were escaping slavery in the South.
Cryptonomicon. Oh god, Cryptonomicon.
Gilver in the Devil May Cry novel.
Mark Twain wrote a short story called Lucretia Smith's Soldier where a woman waits by the bedside of her critically injured fiancée, waiting for the bandages that cover his head to come off. When they do, she realizes that he's not her fiancée and she pitches a fit because she wasted two weeks waiting hand and foot on the wrong person.
- Truth in Television: Tragically, a similar incident to this recently occurred in real life. A hospital erred in identifying the victims of a car crash, leading to the family of a victim who did not survive the crash keeping a bedside vigil over someone completely unrelated to them, without knowing until much later.
  - This was also recycled into an episode of House.
After the events of the first book, in Moon Over Soho former WPC Lesley May has to wear a surgical mask (a modern update of this trope) as a facial support and to cover the horrible facial scarring gained at the end of the previous book, the removal of the mask forms a similar dramatic reveal.

Live-Action TV

Blackadder II: as Lord High Executioner Blackadder has beheaded a man who wasn't scheduled until later in the week; when the executed man's wife comes to visit her condemned husband Edmund pretends to be him by putting a bag over his head.
In Ugly Betty, the boss' sister Alexis has this.
Spoofed on Arrested Development with Lucille Bluth after plastic surgery in one episode; a photo of her "unwrapped" early becomes the model for a successful horror movie's villain.
An episode of Pushing Daisies has this, complete with a drawn-on face.
In an episode of The Incredible Hulk David Banner had amnesia and bandages covering his face due to severe burns - which was quite convenienet since Intrepid Reporter Jack McGee was paling around with him the entire episode. This was the ep where McGee discovered that the Hulk was a normal person who turned into the Hulk.
In The Twilight Zone episode "The Eye of the Beholder," a woman has her face wrapped in bandages as she undergoes treatment for the horrible ugliness that prevents her from living in the dystopian society. When the bandages come off, she's gorgeous... except that a Reveal Shot reveals that all the doctors have pig faces--the treatment has failed and she's still "ugly".
Get Smart: Max impersonates a safecracker by having his head swathed in bandages so the bad guys can't tell he isn't that guy he's pretending to be.
In an episode of Gary Moore's To Tell the Truth, Prankster Alan Abel appeared with his head wrapped in bandages, as it turned out not so much that he wouldn't be recognized, but so the panel wouldn't identify his two impostors -- Larry Blyden and Tom Poston
David Robert Jones, the Big Bad of the first season of Fringe, wears bandages on his face after he gets a terrible skin disease from teleporting from the prison in Germany to Little Hill

Music

Nash the Slash, best known as the mandolin player from Canadian progressive rock band FM, has performed like this since the late 70s, not due to any injury or illness, but as a way to maintain his privacy.

Video Games

1213 wears a mask on his face to help heal the sores caused by the plague that broke out among the clones.
DiZ from Kingdom Hearts covers his face in red bandages, and two belts for good measure, to conceal his identity as Ansem the Wise.
The main character in Sanitarium sports this look throughout the game, due to injuries caused by a car crash.
Joshua Graham, AKA The Burned Man is portrayed as this in Fallout: New Vegas.
Hush/Thomas Elliot in Batman: Arkham City takes this to a whole new level. He wrapped his head in bandages because he cut off his own face. His victims also have their faces wrapped in bandages; he removed their faces before killing them. He eventually unravels his own bandages to reveal that he's stitched together all of the faces he cut off of other people in order to make himself look like Bruce Wayne.

Western Animation

An episode of Batman: The Animated Series had one for a former supermodel who had undergone plastic surgery to make her look younger. The doctors unwrapped the bandages, and when she demanded a mirror (which goes hand-in-hand with the trope), she was horrified by how hideous she looked. She was actually as beautiful as ever, but as a narcissist she could only see her flaws.
- A more prominent example of this: Two-Face, after his disfigurement, has his face wrapped and demands a mirror from his doctor as they're unwrapping it, flinging him across the room when he doesn't immediately comply. We don't see his reflection, but we hear his anguished scream.
There was an episode of Futurama where Leela had plastic surgery to give her a second eye. The entire top half of her head was wrapped. Played with in that the doctor slowly took the bandages off, characters holding their breath in anticipation... only to find out that the first time, they had the wrong woman.
The villainous Master of Disguise No Face from the Action Man toyline and CGI movies.
Git Hoskins in Spider-Man Unlimited of course the twist is the bandages don't cover his body, they ARE his body and he can unravel himself and use the bandages like combat tentacles

Real Life

Mummies, and as a consequence, all mummies ever depicted in fiction. Probably the Trope Maker.