Pokémon: The Team Rocket trio have started doing this in the Unova saga. They most likely switched from a Paper-Thin Disguise to this now that they're more competent.
A Nurse Joy that worked for the Pokemon League Inspection Agency also did this in the episode "Showdown at Dark City," as she went undercover with a trench coat, fedora, sunglasses and a scarf over her face. (She even attempted to drink her tea through the scarf!)
In retrospect, Kotomi's handler in CLANNAD probably shouldn't have chosen this as his everyday clothing, since it made practically everyone think that he's a bad guy and generally made him look really, really suspicious.
Trenchcoat and sunglasses was the disguise Shamal went for in Magical Girl Lyrical Nanoha A's when she was spying on the heroines. She was immediately recognized by the first person who knew her.
Heroic example in the first chapter of Muhyo And Roji, Roji (who also thinks mobile pottery is an effective stealth tactic) wears a trenchcoat and he and Muhyo wear sunglasses while staking out a client in order to locate the ghost of one of her dead friends. Muhyo notices that they "stick out like sore thumbs."
Detective Conan has members of the Black Organization frequently showing up in conspicuously sinister black trenchcoats.
Spy D in Project A-Ko wore this outfit at least until the big reveal of... her... gender...
All the spies in the second Project A-Ko OAV wore the same outfit — a white suit, white fedora and sunglasses. Nobody seemed to notice, though the spies seemed able to pick out who was CIA and who was KGB
Recorder and Randsell: Atsushi's trenchcoat gets him mistaken for either an exhibitionist or a pedophile a lot.
Mostly in older comic books. Many a supervillain wears this over their costume to gain access to the City Bank.
Ben Grimm, The Thing, in the Silver Age, would routinely put on a trenchcoat and fedora, which was sufficient to disguise being an orange rock monster. Later comics justify this by presenting it more as a matter of self-consciousness - the disguise doesn't really work that well, but it makes Ben feel more comfortable when stepping outside.
In one issue of Fantastic Four, when the FF testify at a congressional hearing, a bunch of mentally-manipulated D-grade villains enter the room, dressed in trenchcoats and hats, and attack them.
Hilariously, Iron Man used this disguise once in an early adventure, in about the most implausible scenario one can imagine for maintaining this ruse. Clad in his original, bulky grey armor, his trenchcoat-and-fedora disguise is evidently sufficient to elude all suspicion while travelling to Asia to take on the Mandarin on a commercial airline flight from New York! He opens the door and bails out of the plane over China. (Admittedly, this was before Iron Man's armor was shown as capable of long-range flight, but you'd think Tony Stark would own an airplane or two, at least.)
Namor, the Sub-Mariner, liked to wear these, both as villain and hero. Even more conspicuous for his taste in high quality fabric and tailoring.
The Silver Surfer also manages to look less conspicuous with the trenchcoat-and-hat look.
In Uncanny X-Men #111, the new furry Beast uses this disguise to enter a crowded carnival. Jean Grey lampshades how strange his outfit looks.
A Civil War tie-in issue of Sensational Spider-Man features a story where both The Chameleon and Electro are dressed in a trenchcoat and fedora stalking Mark Raxton's son at a little league game full of children and their parents, in the heat of the summer and no seems at all concerned or suspicious.
Made especially 'wha?' when you consider that the Chameleon's whole hat is incredibly effective disguises.
Almost every main character in Frank Miller's Sin City dons a trench coat at some point. Marv especially likes them and often takes them off of the bad guys he kills. Usually, they are packing guns, spying, sneaking around, or otherwise being conspicuous.
Makes sense, mind you, as the climate of Basin City is driven entirely by dramatic convenience. The winds blow cold and hard to keep all those long coats billowing dramatically, and the slick blackness of the asphalt is reliably maintained by constant rain.
In The Desert Peach, a Gefeldtpolizei casing a Parisian cafe apparently thought he counted as "plainclothes" despite wearing his usual coat and hat, because he was walking a poodle at the same time. This was what convinced Rosen the place was under surveillance. ("No one but a Gefepo would think walking a poodle automatically makes you French!")
Even Godzilla used this trope once, in Marvel's licensed series. To evade pursuers, the Kenny of this series dresses the temporarily-shrunken Godzilla in a hat and trenchcoat. Admittedly, it only works for about two minutes, at night, but it was enough to fool two criminals, who attempt to mug Godzilla (yeah, that goes about as well as you'd expect.)note Godzilla, King of the Monsters #19 (1978)
Every version of Teenage Mutant Ninja Turtles utilizes this to let the turtles walk the city. No one will ever notice that you are a large green turtle if you wear a trenchcoat and a hat!
Parodied in Cattivik when Superpip (a spoof of Super Man) dons himself in one to buy some porn in disguise, claiming that no one will recognize him. In the very same panel, a kid from the other side of the street asks his father "Why is Superpip wearing a trenchcoat?".
Magnesite the alien/youma, a fanfiction creation of one of Beryl's generals from the first Sailor Moon season, becomes so enamored of Humphrey Bogart movies that when he is imprisoned he keeps reviewing them in his mind to avoid death by boredom. The result several hundred years later is a person who uncontrollably acts like the Bogey, spending his (unlife) trying to bring private detective work and noir to sparkling-white Crystal Tokyo. His trenchcoat is his trademark, something all the Senshi know.
Ferrite, also a fanfiction creation, is a cursed human from the Silver Millennium who keeps being reincarnated throughout history until he finally meets up with the Sailors in Sailor Moon. His former Guardian powers change into a trenchcoat with infinite pockets, the ability to throw yellow roses from the trenchcoat similar to Tuxedo Mask, and he uses an ancient blunderbuss that can kill with one shot. Ferrite's alter ego calls himself Trenchcoat Mask in the modern day.
Films — Animated
Megamind: Megamind's Brain Bot's hide under a trench coat and fedora in a crowd during the opening. It is bookended in the conclusion when we see Metro Man using the same tactic.
Nigel Small-Fawcett:(yelling) Mr Bond! I say Mr Bond! Nigel Small-Fawcett British Embassy Nassau."
James Bond: Nice to meet you Nigel.
Nigel Small-Fawcett: Sorry I'm late but as your one of these undercover jollies I took the precaution of not being followed.
James Bond: And that's why you shouted my name across a harbor?
Nigel Small-Fawcett: Oh god did I? Oh I'm sorry! Damm! Damm! Sorry I'm rather new to all this!
In X2: X-Men United, Nightcrawler uses a trenchcoat, cap and dark glasses to sneak into the White House. Remember, your taxpayer dollars go to the guys whose job it is to stop suspicious threats like this. Although it does help that he can, ya know, teleport past any checkpoint.
Spider-Man: Doc Ock walks into a bank using this technique. It actually made sense though, as a trench coat would be about the only way to hide his mechanical arms and maintain the element of surprise.
Used as a Visual Pun in Mel Brooks' Silent Movie. The title cards announce an upcoming Sneak Preview of Mel Funn's film. Cut to the theater, and the entire audience is sneaking in, dressed in trenchcoats and fedoras.
Used by Wrong Genre Savvy hero Woody in the Disney film Condorman after he persuades his friend Harry to let him go on a CIA courier mission despite the fact that he's a comic book writer, not a spy. Hilarity Ensues.
Knowing features the creepy Trenchcoat duo, who follow around the kids. Nothing suspicious about that...
Back To The Future Part II gets a quick shot in at this. Doc and Marty arrive in the past trying to keep Biff from getting the sports almanac, Doc hands Marty some age-appropriate money saying, "Get yourself some fifties clothes." As Marty runs off, he screams, "Something inconspicuous!" Cut to Marty wearing a leather jacket, fedora, and sunglasses. Never mind that this makes him look more like a Michael Jackson impersonator than anything else.
The Tiger Makes Out: Eli Wallach's character, preparing his campaign to disrupt the indifferent, sheeplike world around him, picks up a trenchcoat and fedora at a pawn shop. As the owner anxiously watches him suiting up, he points out that he has a sawed-off shotgun for sale.
Rodney Skinner, the Invisible Streaker from The League of Extraordinary Gentlemen, wears a black ankle-length trenchcoat, a matching fedora, and pince-nez sunglasses. The conspicuous part comes in when he doesn't put on his greasepaint makeup, and thus the ensemble appears to be floating along all by itself.
"How come in movies no one can ever see past a trenchcoat and a fedora hat? Is it like Clark Kent's hypnotizing glasses or something? Do they just make people stupider?
Le Samourai: The main character's choice of unsuspicious-looking clothes is a trenchcoat and fedora. It makes sense in the setting, but even if it didn't, Rule of Cool would turn this trope into something more like a Badass Longcoat situation.
There's a medieval parody of this in the Terry Pratchett book Going Postal- one of the main antagonist's less reliable partners gets drunk one night and comes to unburden himself to the Big Bad. Upon the partner's arrival, the villain's servant asks something like "May I take your highly conspicuous hooded cloak, sir?"
One of Geronimo Stilton's old friends is described as always wearing a trenchcoat and dark glasses; quite naturally, he's a secret agent. Oddly, Geronimo reveals that his friend has always worn a trenchcoat and dark glasses since the first grade.
The ducks in St. James's Park in Good Omens have gotten very good at identifying the many, many secret agents who meet there by their conspicuous "disguises."
"The ducks in St James's Park are so used to being fed bread by secret agents meeting clandestinely that they have developed their own Pavlovian reaction. Put a St James's Park duck in a laboratory cage and show it a picture of two men — one usually wearing a coat with a fur collar, the other something sombre with a scarf — and it'll look up expectantly."
Discussed in Lemony Snicket: The Unauthorized Autobiography. After giving a lengthy description of the contents of the VFD disguise kit, the narrator mentions that the only piece they haven't figured out how to use in a disguise is the medium length beige trenchcoat.
Lampshaded in The Dresden Files. Harry is often wearing his long leather duster, and notes that it makes him look odd and conspicuous, especially when he wears it in the summer. Of course, his leather duster is enchanted to withstand magical and ballistic assaults, so when he's on a case (and thus runs the risk of someone trying to shoot him), he's going to wear the damn thing even if it's 95 degrees out.
In the non-fiction book The Cuckoo's Egg, Clifford Stoll worries that people at Berkley will realise he's meeting with the notorious Central Intelligence Agency (about a hacker involved in espionage) due to their conspicuous trenchcoats. When the CIA do turn up, his colleagues instead think they're IBM salesmen due to their conspicuous suits and ties.
Kids Incorporated: "The Bully" - After angering a local bully, the Kid sneaks into the P*lace wearing a trenchcoat and fedora, which effectively hides him in a crowd whose median age is 13.
Recycled five years later, only this time, it's newcomer Robin sporting the trenchcoat for the same reason.
Chuck vs. The Third Dimension A man in a dark trenchcoat, hat and dark glasses carrying a suspicious package plants a bomb in the BuyMore. Chuck is the only one to notice that this is an odd way to dress in a Burbank summer.
Somewhat toying with the trope is at the end of the episode, the bomber tries again at a crowded concert, only this time he's paid several people to dress in matching trenchcoats to lure Sarah and Casey while he wanders around undetected in a business suit.
Ze Resistance from 'Allo 'Allo! all wore a conspicuous macintosh and beret combo.
Angel and Spike sometimes hide underneath their trenchcoats so they walk around in the sun.
Lampshaded on Angel where Gwen immediately spots her secret informant by the fact that he's the only person in LA wearing a trenchcoat.
Subverted in the NCIS season six two parter, "Cloak and Dagger". The pickup man for an espionage operation shows up as pictured above, and is instantly made. However, his inept attempt at being inconspicuous manages to help convince them that he was an innocent pawn rather than the mastermind behind the operation.
When Dexter is training Miguel in how to murder people, he notes that he told him to be inconspicuous. Instead he "turns up looking like the Unabomber" (with baseball cap, black sweater and sunglasses), especially conspicuous since they're in a casino at the time. In contrast, Dexter always wears a beige sweater and pants when on the hunt.
When Joey Snake and Wheels try to use a fake ID to buy beer they try putting a trench coat on Snake the tallest of the three in an attempt to make him look older. It fails partially due to the ID being especially fake but mostly due to the fact that they were only fourteen and while they were closer to the legal drinking age of 18 at the time it was still quite a stretch.
Lampshaded on Yes, Minister when Bernard, after saying too much to the press, attempted to sneak past reporters in a trenchcoat, hat, and shades. On the hottest day of the year, according to the novelisation. Needless to say, the press were very interested in this strange man entering a government building.
Used a lot by Sylar in season one of Heroes, though Sylar wore a baseball cap instead of a fedora.
In the video for Golden Earring's "Twilight Zone", the protagonist is stalked by spies who also sing backup vocals. You can tell they're spies, because they're in trenchcoats, fedoras and dark glasses.
Adventures in Odyssey: In "Heatwave" Jack tries to follow the "mystery kid" for the better part of the episode, but Mr. Watson points out that rather than appearing casual,he in fact really sticks out because of the trenchcoat that he's wearing in the middle of a heat wave.
In Liberal Crime Squad, Trenchcoats are both "stealthy" gear (meaning who wears them tries to hide instead of disguise as the enemies when infiltrating) and the only type of clothes large enough to conceal mid-sized weapons like a shotgun or light machinegun.
In the Eastern Europe level of Metal Gear Solid 4, Snake dons a trench coat and face camo to get past Raven Sword's station check point. In a subversion, his face is immediately added to the PMC's blacklist, rendering that disguise useless. This is played even straighter if you notice someone (later revealed to be Scarabs) in a trench coat and hat following Snake, who immediately disappears every time you investigate.
His facial disguise was not the greatest, it must be said, since it was simply a de-aged version of his own face. At least he took off the bandanna...
Carmen Sandiego not only wears a trenchcoat and fedora, but a fire engine red trenchcoat and fedora. On the other hand, she is motivated by showing off.
She takes advantage of the inconspicuousness by somehow arranging other non-criminal women in trenchcoats to visit the area near ACME Headquarter so that she could more easily rob it.
The Spy in Chip's Challenge, who steals all your tools if you run into him, wears sunglasses with a blue fedora and trenchcoat.
Veronica from Fallout: New Vegas wears a thick, hooded cloak. It would work as a disguise in a fantasy game, but it's pointless in a sci-fi. Set in a desert. And people still recognise her.
In her defence, she doesn't seem to be trying to disguise herself, and there is precedent for people walking around with thick, hooded cloaks in the neighbouringregion.
Albert Wesker of Resident Evil fame dons a trenchcoat in the fifth game of the series. But by then he's far less "conspicuous" and more of a darwinistic Card-Carrying Villain.
MAG ISA — We got fourpeople with guns and trenchcoats enter a school. It seems nobody even noticed them. Otherwise, don't you think the cops should be called to stop them before they do a shooting rampage?
While Trudy of General Protection Fault was making anonymous calls to Clifford Myers of Funny Farm in a crossover, she wore a trenchcoat to disguise herself, the brand name of which lampshades this. Oddly enough, The German, an expert at impersonating people who works for CRUDE, uses this in his first appearance while stalking Sharon and Craig.
Sluggy Freelance: Agent Hong mistakenly sees this trope (minus the fedora) in the chapter "Aylee". "You have a surveillance photo from the military jet showing this guy leaving the scene where radar had tracked the entity moments before. You can't tell what he's carrying. You can't even tell it's a he. A long blond wig and a trenchcoat in a grainy photo? It could be anyone!" ...Except that it's Riff, who always looks like that, rather than here being in disguise. And they can't even see he's also got sunglasses.
My Life as a Teenage Robot "Mama Drama"; Jenny, Brad and Sheldon follow Marty into a bank wearing trenchcoats and fedoras in an attempt to evade suspicion. Tuck tags along wearing a pink bunny mask. Their attempts at remaining hidden don't exactly evade notice.
League of Super Evil: the titular team is trying to get into a restaurant. A man who looks exactly like the team in a trenchcoat walks in, and the maitre'd lets him through. Then, per trope, comes another guy who looks exactly the same except for a slightly different visor, giving the same name. And he's the actual League, wearing goggles.
Callisto wears one while spying on a skateboarding event, using it to go near Evan and warn him not to drink an energy drink that will poison him. Given how Callisto's hardly the most non-human-looking mutant and that she's at an event filled with wild teenagers, one has to wonder how the trenchcoat makes her less suspicious than the eyepatch she wears.
On an episode of Pound Puppies (2010), Niblet and Lucky use coats to sneak into a basketball stadium. Niblet hid three puppies (out of five that the crew is trying to get adopted) in his coat. Lucky hides the other two puppies in his coat, while Cookie hides Squirt and Strudel in her dress.
In Hey Arnold!, Helga attempted to sneak into her therapist's office wearing a trenchcoat and a fedora, only for Phoebe to spot her out.
In The Ren & Stimpy Show episode "Hard Times for Haggis," the titular washed-up character sees someone disguised this way purchasing a doll of Haggis that had been gathering dust in an antique shop. Haggis follows the mysterious buyer into an alleyway and sees him rip off his disguise, revealing to be Haggis's runaway Scottie dog Whacky!
When Wile E. Coyote gets hold off a Spy Kit in "Sugar and Spies", he starts wearing a black trenchcoat and hat. In the middle of the desert.
Boris the Burglar◊, the image used in Neighborhood Watch signs is a silhouette of a man wearing a trench coat and fedora.
From a child's perspective: "Mom! That sign says 'No Cowboys!'"
From this (NSFW) Everything2 node: "Now, as everyone who has worked an ER knows, trenchcoats are bad, especially in the summer. This trenchcoat was especially bad, since it was moving and hissing."
When not on stage, Malice Mizer/Moi dix Mois guitarist Mana shows mild to moderate symptoms of this. Most pictures of him in public show him with a large hat and sunglasses, combined with, at various points, large, dark scarves, tops, skirts, boots and- yes- trenchcoats. Due to his habit of Alter Ego Acting, it isn't publicly known whether he dresses like this to try to avoid attention or whether he just likes the style, but it's most likely to be the latter, because his clothes do a pretty pants job at masking his identity. If anything, they make him more recognizable offstage.
Victor Suvorov, a former Soviet GRU agent, says that among the first rules they were taught was - no sunshades, no raised collars, no hands in the pockets. After all, why should they look like spies if they are not spies but Soviet Intelligence Agents?
Ironically, secret police in Hungary and other Eastern Bloc countries would wear the hat, trenchcoat and shades so that civilians would know them for what they were.
Trenchcoats, if seen in real-life and not used for obvious comedic effect, are often associated with exhibitionism or a Coat Full of Contraband.
The icon for Google Chrome's incognito mode is a guy in a trenchcoat.