"When the darkness fell, New York City became something else, any old Sinatra song notwithstanding. Bad things happened in the night, on the streets of that other city. Noir York City."
Niihama, and especially Etorofu take this trope Up to Eleven in the movie Innocence, which borrows heavily from the Film Noir tradition in its visual style.
Neo-Tokyo in AKIRA is a classic and influential example in the genre. It is interesting the compare the colour pallet: Neo-Tokyo evokes the vibe while being much more colour-rich than the typical western example.
Zig-zagged by Tekkon Kinkreet's Treasure Town. It doesn't really look like a City Noir during the day — on account of all the sunshine and life. It is much less depressing than most examples — but it's definitely run-down, dangerous, and filled with people who can't stand living there.
Bubblegum Crisis was heavily influenced by Blade Runner, so the bad sections of Mega Tokyo have a City Noir look.
Silent Möbius is another series that inherits much of its city design from Blade Runner.
Central City in The Spirit. Likewise Indigo City in Tomorrow Stories' Greyshirt feature, which is heavily inspired by The Spirit.
This is the setting for virtually all of the Marvel Noir books, the only exception being Iron Man Noir and Weapon X Noir. Nighttime, rain, guns, lowlifes, the works.
Another Fritz Lang film, M, also fits. It's a city where a paranoid citizenship have begun to attack anyone and everyone in search of a child killer, and the gangsters and police think dangerously alike.
Dark City is this setting taken to surreal heights through deliberate use of Diesel Punkby the city's alien overlords.
Every location in The Matrix trilogy, both in the real world and the simulated one, seems to be either one of these or a Wretched Hive.
Discworld - Ankh-Morpork, particularly the Shades are a Bamboo Tech medieval version of this.
Seen in many of the books and stories by Philip K. Dick, but particularly noteworthy in Do Androids Dream of Electronic Sheep,Flow My Tears The Policeman Said, and A Scanner Darkly.
Rapture in BioShock, especially in its state of decay. Going one better than constant rain, it is underwater. Even better, its leaking in a lot of places.
Max Payne gave us the best early example: nothing like New York, a winter storm, and some Norse ethos to get the noir blood running...
The first level from The Punisher game from 2005 begins with a monologue about how even though the politicians have tried to clean up the city, all they succeeded in doing was pushing crime to other neighborhoods.
City 17 in Half-Life 2 was this on concept art in early stage of development, and it picked up a strong Eastern European inflection in the final work.
Detroit (again) from Deus Ex Human Revolution, along with Hengsha in Shanghai, in somewhat different styles. Detroit is very obviously based on Blade Runner's LA, and Hengsha looks more like Midgar. New York from the original might have counted, too, but we don't get to see much of it, and it's too poorly-rendered to tell.
The urban locations in Kingpin: Life of Crime. Features everything between desolate ghettos and classy, but equally vile Radio City with it's Art Nouveau architecture (bearing a suspicious resemblance to some places in Payback). Also noteable for a weird mix of modern as well as 20's, 30's and steampunk-scifi styles (Cypress Hill music, Tommyguns, and thugs with cybernetic facial modifications all in the same setting!)
The City of Steelport in Saints Row: The Third has art deco and industry seemingly running everywhere, and half of the time the game spawns you at night. Or in the rain.
Bezoar City of the obscure Cyber Punk shooter Hard Reset is perhaps the vastest, most towering example to be found on this page. When we say towering, we damn well mean it too; at certain points the wind whistles by fast enough to suggest you are a very... appreciable distance from the ground that you most definitely can't see. Yet, when you look up? There's still a lot more city to go. At least once you will go down the street through an industrial complex, only to find yourself on the ledge of a skyscraper.
Web Comics
The Ciem Webcomic Series has a bit of a subversion in Dirbine, at least atmospherically. Almost everything appears to happen in the early afternoon or at sunset, when not at night. (Justified: only so many looks are easy to obtain with the game software.) And it's very seldom cloudy or rainy. In fact, most of it looks like it'd be a nice place to live. Yet, all the attitude of a noir setting is present. This one may definitely double as a Wretched Hive.
Batman: The Animated Series relies heavily on this trope for the stylistic views of Gotham City. And yes, it is often night, but that's when the bats take wing...
While the daytime shots of Republic City in The Legend Of Korra are very beautiful, it turns out that the city hides a dark underbelly of crime and poverty. In particular, the night fight scenes in the streets take ques from this trope.
Last Res0rt's City of Wonder. (although at least in terms of being a darkly colored city, they have the excuse of it being located inside a freakin' space station, so any sunlight or other weather that exists there is manufactured anyway...)
Post-Motor City Detroit is almost always portrayed this way.
Victorian London is often portrayed this way. Noir fiction can drawn on Victorian London.
Post-Soviet Moscow fits the trope perfectly, both in works like S.Lukyanenko's Watch tetralogy and in Real Life. The climate is dark and cold for nine months and blisteringly hot for the remaining three, the architecture consists mostly of drab Commie-era concrete towers with some neo-gothic Stalinist skyscrappers added downtown and a lot of squalid 'khrushevka' apartment houses in the outskirts, the citizens are apathetic, the Corrupt Corporate Executives are flamboyant jerks and the psychological athmosphere of the place was nasty enough even before the global financial crisis, and now it's downright unbearable. St. Petersburg is similar, but with extra gloomy clouds and extra gothic. Other Russian megapolises too — but with less decadence and more, often much more, of the city on the Wrong Side of the Tracks.