An area of strip joints, brothels and other seedy locales. Very much based on reality - the term came from railroad workers leaving their red work lamps outside the businesses they were patronizing when going into town for the evening so that they could be located if they needed to be called back to work on short notice (Guess where the lamps were usually found).
Generally portrayed in one of three ways in fiction:
The liberal version: Drunk happy people, women waving down from balconies. The protagonist gets to have a good time, or gets made fun of for being unable to. The most friendly take on the district.
The pitiful version: Drunks collapsed in the gutter, battered strung-out prostitutes. The protagonist is probably here on business. Possible location in a Wretched Hive. Very common in cop shows and Antihero comics. You're most likely to see this side of the district in the grey light of the morning.
The hostile version: The drunks will pick a fight with you, the women will rob you or knife you in an alley. Possible location in a Wretched Hive. The protagonist is either lost or hopelessly naive, and will be wishing he'd found version 1 before the end of the night. Also common in cop shows, particularly in the first five minutes when they're showing the soon-to-be victim.
Compare Band of Brothels.
In one scene in Evangelion 1.0, Shinji wanders past one. He is so lost in his own depression (also his SDAT player) that he's largely oblivious.
The Yoshiwara district of Tokyo is mentioned from time to time in Ooku. Shogun Iemitsu downsizes the Inner Chambers and restocks the decaying pleasure district with desirable men after a gendercide plague destroys the market for female prostitutes and leaves only dregs of men. The Reverend Kasuga earlier hired a few women from there for a plot.
The brothel in Dejima is the last one in all of Japan to still employ female prostitutes to cater to the Dutch sailors. It's noted that on the Christian Sabbath the male prostitutes have the day off to wander the streets alongside the foreigners to hide the fact that Japan is a Lady Land.
Downplayed in Heat Guy J. Kabuki Road does have (or is implied to have) brothels, strip clubs, etc. but there is other entertainment, too.
Kamisama Kiss has a demonic version of the Red Light District that Tomoe used to visit often before Nanami showed up. How often? Well, he knew all the Tanuki prostitutes by name and they treat him like he is almost family.
In Piano No Mori, the town where the story takes place has a Red Light District where one of the two main characters lives. It is called "The Edge of the Forest" due to its location.
These appear in a few episodes of Panty & Stocking with Garterbelt, including one where a ghost parodying Little Red Riding Hood would lure unsuspecting people in for her wolf companion to kill.
The main characters in Gintamalive in one. Yoshiwara also shows up as a literally underground red light district.
Tomoko visits one in chapter 28 of WataMote, hoping to get a job as a hostess there. She gets scared by what she sees there and, after getting a phone call from her mother, decides to give up and come back home.
Saiunkoku Monogatari: Shuurei worked as an accountant at Kougaro, the number one brothel in the red light district, as one of her various jobs; she's actually close friends with Kochou, the manager of Kougaro.
Old Town from the Sin City series. It fits into the "hostile" version of this trope.
It doesn't really fit into "hostile" within the story, as the prostitutes (ruthless as they are) would only knife you if you try to harm them (stiff them, and they'll do worse). The protagonists find allies there, and the soon-to-be-victims shown were actually dirty cops who were up to no good. Old Town is actually a place of law and order, compared to the wanton lawlessness and corruption of Basin City. It pretty much is a subversion of the hostile red light district.
The Metabarons Universe feature Cities containing a "red ring" in the center and act like the local red light district.
The East End in Gotham City, where Catwoman made her home during the run of her book and Batman himself considered it a lost cause.
Rorshach walks through such a neighbourhood in Watchmen lamenting the passing of "American Love" as he is offered the Swedish, French etc. versions.
Bruce Wayne gets into a fight with a pimp in such a location in Batman: Year One. One of the pimp's girls is the future Catwoman.
A Red Light Area is the location of a porn cinema shooting by a nervous little Catholic boy in The Dark Knight Returns
The protagonist is taken to one of these in Welcome to the Brothel by his squadmates so that he can lose his virginity.
Glitzville is portrayed like this in the remake of Yu Gi Oh The Thousand Year Door. It's tamer than most examples of this, but still far from innocent. Stan describes it as “A city of sin… but suspended in the heavens… A place of contradictions if there ever was one…”
Most Naruto fanfiction that don't have the title character living in the slums, have him living in the red light district. Usually the first version but sometimes the second or third.
The Card Captor Sakura fic Shadow of the Dragon features the red light district of Shibuya as the third version in chapter 13. The brothel members are described as having been "trained" by the pimps, who state that one has to break a girl to make them a "good whore," and has a waitress described as not looking old enough to drink the alcohol she serves. Sakura's mother Nadeshiko was kidnapped by the employees there, but her friends raided the building and rescued her before anything truly unfortunate happened.
The Red Light District of New Orleans in the early 1900s is heavily featured in The Meq, though it doesn't really fit into any of the above three categories because it's shown so realistically.
The city of Ankh-Morpork in the Discworld books has an area known as the Street of Negotiable Affection, which is maintained by the Seamstress's Guild. Renamed from "The Whore Pits" after much representation from said Guild.
George Alec Effinger's Marid Audran series takes place in the Budayeen, which is a cross between this and The City Narrows, in a Cyberpunk Arab/Muslim setting. Prostitution and drug dealing are rife, but tourists who dare venture in often don't make it out.
The caravanserai area of Vorbarr Sultana in Barrayar. By the time of the later books in the series it has been cleaned up and gentrified (but you can still get into trouble in some of its back alleys.)
The Spenser novel Ceremony includes a very grim view of Boston's Combat Zone.
There is one in Eva Luna; the title character spends some months as a protegèe of La Señora, the local and most influential Miss Kitty in the district itself. It's described as a relatively pleasant place where, despite the sometimes downright illegal activities in there, the residents are basically decent people who treat the sex industry merely as a way to support themselves. When the new police leader breaks their implicit deals with the workers and tries to impose abusive bribe fees, Eva's trans sexualCool Big Sis Melecio attempts to fight back and get support from the residents. It backfires horribly and the district ends up being "invaded" and disbanded; La Señora has to run away, Melecio is incarcerated, and Eva is thrown back in the streets.
The city of Sharn, in Eberron, has three red light districts — a tacky and tawdry one, a middle-of-the-road one with the biggest changeling influence, and an arguably tasteful one.
In Exalted, the Demon City has a gold light district. This is because gold is seen as an obscene color in hell due to its association with the sun. Also, the district is a very powerful demon in her own right.
Most such locations in Exalted are blue light districts, the colour chosen to honour the Maiden (ahem!) of Serenity. In fact, the Maiden of Serenity's office is one of these, as it's modeled after the first whorehouse in Creation and still serves as a bar, whorehouse and opium den while also serving as a divine government building.
The musical Tenderloin features a historical example from the Big Applesauce.
The musical Les Misérables features the song Lovely Ladies, which involves prostitutes singing about their occupation and is set in what is meant to be one of these. Starts off as the "happy" version and gradually segues into the "pitiful" version.
Dragon Age II: Kirkwall has the fantasy equivalent of this, the "Red Lantern District". It contains the Blooming Rose Brothel. Therein lies an apostate mage (or as Isabella calls her, an 'Apostitute') that uses mind control on Templars.
Final Fantasy VII's Wall Market in Midgar is mostly the liberal version, with a dash of hostile. It's a lot more inviting than the rest of the slums, and the girls at the local sex hotel don't seem like they're suffering from much psychological damage (the player even gets to read what they're thinking). However, the district is run by a crime lord named Don Corneo, and it's heavily implied that women get kidnapped and forced into prostitution on a regular basis. On your first visit, one of the NPCs even suggests that you sell Aeris off to the Don.
And why are Aeris and Cloud there, anyway? They're trying to find Tifa, who apparently was abducted and taken to Don Corneo's presence. She's actually going undercover to investigate him.
Raidou Kuzunoha vs. The Soulless Army has one. It's important all of one time, then it's only good for dialogue collecting. Oh, and some careless person left a whole clip of fire bullets in front of the giant lamp.
The Futurama video game has a level in the Red Light District.
Would you believe there's one of these in Professor Layton and the Diabolical Box? Layton and Luke catch the owner of the Molentary Express, Mr Beluga, walking into a cabaret and attempting to converse with the woman standing outside. Not only is she one of the show-runners, but she hits on Luke (who's only twelve) after hitting on Layton. Also, there's a cop standing outside the area (which has red lighting on the map) who refuses to let the young boy in so the player has to go the long way around.
Its The Old Republic incarnation also has a Red Light Sector as a questing zone. The main adversaries are members of a gang that kidnaps people, cuts out their organs, and uses the resulting bits to create high-tech implants and genetech.
Duke Nukem 3D Episode 1 Level 2 is called Red Light District. It contains a porn shop complete with private video booths, a bar, and a strip club.
Circuits Edge, the 1989 CRPG, was based on George Alec Effinger's Marid Audran novels (see Literature, above), and like them is set in the Budayeen, a Red Light District.
In Infamous 2, a large Red Light Center can be found in New Mirais, with a large central building modeled after an old riverboat.
Bioshock 2 features Siren Alley, the Red Light District of Rapture. Ironically, Siren Alley was originally a high-class part of Rapture, where architects and skilled laborers lived and displayed their work, before the work dried up and caused the whole area to fall on hard times.
In True Love Junai Monogatari, you can hang out the RLD of the fictional city of Meiai, which seems to be similar to Tokyo's Roppongi or Kabukicho districts. If you're going for Good Bad Girl Mayumi's route, you must bump into her there and right next to a local Love Hotel.
In an episode of The Simpsons, Homer is asked to take the dog to the vet to be neutered (after the dog had fathered a litter of puppies in an episode parodying 101 Dalmatians), but he feels bad for Santa's Little Helper. So Homer takes SLH to the Red Light District of Springfield, which has not only porn theatres, prostitutes, etc. for the human men, but also for dogs to enjoy. Homer even pays to play air hockey with a prostitute while SLH has some "fun" with her dog.