Gloves are a curious accessory. For participants in some occupations (medicine, construction, gardening) and sports (boxing, riding), gloves are essential or at least recommended. They're also commonly worn in cold climates or seasons, and in some historical periods, social customs require people to wear gloves. Most of the time, however, the wearing of gloves is unusual, and it's even more unusual for a person to wear only one glove.
When this trope is operating, a character is depicted wearing a pair of gloves (or a single glove) without the excuses of occupational demands, low temperatures or social custom. If the glove is worn only on one hand, it is always the same hand. Wearing the gloves will set the character apart from others in the work, and there's generally plot-relevant reason for their presence. Most often, the gloves serve to conceal something about the wearer, though occasionally they're worn for protection and/or style. The gloves might be worn to conceal a Red Right Hand, hide an injury, cover a prosthesis, disguise a social stigma, or simply to indulge personal preference.
Similar to Sunglasses at Night, wearing a glove or gloves at all times is both cool and conspicuous.
Anime and Manga
In Neon Genesis Evangelion, Gendo always wears gloves, and they cover burns he receives in an early episode rescuing Rei. He later has an embryo Eldritch Abomination implanted in one of his hands, which make the gloves even more necessary.
In a variation, Danzo covers his whole right arm in a metal contraption, which is covered further by having his arm tucked into his kimono. It hides a multitude of transplanted Sharingan on said arm, alongside the fact that he injected The First Hokage's DNA into said arm, making it look hideous (with Hashirama's face seemingly grafted on his shoulder).
Danzo has a Sharingan beneath his bandaged eye.
Kakashi has a Sharingan left eye that he covers with his headband (because opening it eats up his chakra reserve)
Ao from the Mist Village has a Byakugan right eye covered by an eyepatch.
In Darker Than Black, Kirihara's superior always wears gloves. Turns out he has prosthetic hands.
When the team enter a hotel, they find the manager as a little old lady who bandaged her left hand because of a burn. It's really a cover-up and the covered hand is also a right hand, revealing her as also the mother of the man Polnareff was looking ofr and killed before this incident.
DC Comics' Heroic Fantasy hero Claw the Unconquered had a literal demonic hand, hidden under a red glove to reduce its evil influence on him.
Several X-Men characters wear gloves associated with their powers.
In his early appearances, Wolverine had his claws attached to his gloves. Once they were said to come out of his hand, his gloves had slits to accommodate their extension.
Gambit also wears gloves. His touch allows him to change the potential energy of objects he touches into kinetic energy; his gloves have a few fingers open or missing so he can "charge" and manipulate his cards (one of his weapons of choice). That said, the gloves' design is also cool.
Film - Animation
Wybie (and the Other Wybie) in the film adaptation of Coraline. In Real Wybie's case it may be down to the fact he's seen riding a bike most of the time. That and there's a poison oak bush near the Pink Palace. Later in the film Other Wybie removes his glove to show Coraline he's just sawdust.
Film - Live Action
The Invisible Man (starring Claude Rains) is set in winter, so gloves don't really look that odd until he goes indoors and doesn't take them off, or later on when he's also wearing pajamas and a robe. The Vincent Price sequel (1940's The Invisible Man Returns ) is set in warmer weather, so it looks a bit stranger for him to wear them in most instances. The title character of The Invisible Woman (also released in 1940) can get by with it more considering the social customs of the period included women wearing gloves (and hats, for that matter), so it doesn't stand out so much.
In Son of Frankenstein (1939), Inspector Krogh has a prosthetic arm (having lost his right arm when a child, the Monster tearing it off the boy) and he wears a glove on it indoors and out. He does remove the left glove in some indoors scenes There's a bit of black comedy when the actor (Lionel Atwill) sets the position of his right arm with his left hand to "demonstrate" the right arm is prosthetic.
In Who Framed Roger Rabbit, Judge Doom wears black leather gloves all the time, but he puts on a larger rubber glove in his first appearance to Dip some poor Toon. Later it turns out they also hide the fact that he's a toon himself.
The protagonist in V for Vendetta wears gloves and a mask at all times because he was tortured and disfigured as a prisoner.
In Funny Games, two clean-cut young men wear white gloves, making them look a little like golfers. The wife asks about them because they didn't take them off inside of the house, and Paul claims he has eczema. They wear them to hide their fingerprints.
While it would make sense to wear gloves often anyway, since he's in the cold North, Jon Snow wears gloves at all times anyway, because in the first novel, he got a burn on one of his hands.
The smuggler turned knight Davos also wears gloves at all times, because in the interest of "justice", Stannis rewarded him by knighting him, but also felt it necessary to chop off all of his fingertips on one hand as punishment for his earlier crimes.
In Making Money, Cosmo Lavish wears gloves to hide the ring he wears, both because it's stolen property and because it's made of stygium, a metal that glows white-hot in sunlight.
In the Ciaphas Cain novels, Cain wears gloves. Technically they're part of his uniform, but they also serve to hide his prosthetic fingers.
In The Curse Workers, as the powers can only have an effect through skin to skin contact, so everyone in this world wears gloves.
Curly in Of Mice and Men wears a glove full of Vaseline on one hand, supposedly because he's keeping that hand soft for his wife. This has no plot-relevant reason, but does make the theatrical adaptation easier to stage when his hand gets crushed.
In an episode of The Dick Van Dyke Show Rob & Laura are about to go to a formal dinner on behalf of his boss Alan Brady to accept an award from a black group, but they both accidentally dye their hands black. They decide to wear gloves to the event, but Rob 'fesses up during his speech. The audience at the dinner find it funny rather than offensive.
In the Outer Limits episode "Demon with a Glass Hand" the man with the glass hand wears a glove over it, only removing it to speak to it or add a finger as he finds them.
In the 2006 Granada-WGBH co-production of Agatha Christie's Towards Zero, a character named Thomas Royd (played by Julian Sands) wears a glove on his useless right hand. He's asked about it at a dinner, and he explained that he got caught in a doorway during an earthquake when he was a child.
In one episode of Alphas the villain wore a glove to conceal his deformed hand, which could upon contact control minds.
Bridge in Power Rangers S.P.D. wears gloves most of the time, only to take them off to use his powers (the real world reason is to cover up the actor's tatoos).
Dexter: Serial Killer Killer Dexter sometimes uses rubber gloves when he searches for evidence in his future victims' places, but at times he uses ordinary gloves. Once somebody sees him coming home with the gloves on and points out that Miami is little too hot for wearing them.
In Downton Abbey, Thomas intentionally gets his hand shot through with a sniper's bullet, earning him a deferment. He returns to the Abbey wearing a black glove to hide the scarring.
In Mitsumete Knight, Raizze Haimer, one of the winnable girls, wears a pair of red gloves at all times (to the point one of the other characters, the young Laury Callwell, affectionately calls Raizze "Tebukuro no Onee-chan", i.e. "Gloved-Big Sis"). There's a reason behind this: She's one of the eight enemy generals of the game acting as The Mole, so she has to wear them in order to hide the bedsores and scars her hands have due to constant sword-training. The red color of the gloves is also a Foreshadowing, as the symbolic color of those generals is red.
In Aladdin: The Series, the Evil Sorceror Mozenrath wears a magical gauntlet that stripped the skin and flesh from his hand as a price. Under the gauntlet, his hand is just bone.
In Dexter's Laboratory, Dexter's mom always wears gloves due to being a germaphobe. This was explained in one episode.
Kiff in Futurama. In one episode, he ends up accidentally touching Leela when his gloves come off and gets impregnated by her (his species reproduces by touch). Although the wearing of gloves is simply down to part of the uniform he and Capt. Brannigan wear.
Harold Lloyd lost a finger in an on set accident early in his career and had to wear a prosthetic glove for the rest of it.
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