Road House (1948) - featuring Ida Lupino singing, and Richard Widmark’s scenery chewing.
Dark City - Featuring Jack Web as a bad guy.
Sirocco - A poor man’s Casablanca.
The Strange Love of Martha Ivers - Some might call it more of a Film Gris, but it is a charming film with Van Heflin.
They Drive by Night - Bogart playing second banana to George Raft in a film about truckers in trouble. Also featuring Ida Lupino.
White Heat - Possibly Cagney’s best, though with the usual outcome for his charcter.
Johnny Angel - Sucks, but you should see it anyway. George raft spends twenty minutes looking for a dame, and when he finds her he stands there glaring at her, never bothering to mention that he’s actually there to protect her. A classic. And it’s got Hoagy Carmichael.
Wikipedia’s list of 35 notable Film Noir movies.
The Cheap Dectective.
After you’ve seen Casablanca, The Big Sleep, the Maltese Falcon and To Have and Have Not. 
Key Largo, for the Bogie Bacall thing - possibly the most mature of the Bogie Bacall films - Lauren playing something other than the sex kitten. OK, still a little bit.
Asphalt Jungle - early Marilyn Monroe.
Notorious - film noir meets WWII spy movie.
Just watched this a few weeks ago. It’s hilarious hearing Fred MacMurray refer to Barbara Stanwyck as “Baby” at the end of every sentence. But otherwise, great noir.
And I’ll second Key Largo: Bogie and a bunch of gangsters, stuck in a hotel during a hurricane. What’s not to like?
Has somebody already mentioned Detour? Great low-budget noir.
Kiss Me Deadly, with Ralph Meeker as Mike Hammer. Cold War noir, with Mike Hammer kickin’ ass – not taking names, though. He doesn’t really care what your name is. Still gonna get your ass kicked, though – and it’ll stay kicked. Also, he’s got a really up-to-date apartment, with a machine that takes phone messages when he’s not at home.
Sin City is what I call hypernoir.
Most of my favorite classic noir have already been mentioned, including Out Of The Past, Double Indemnity, Touch of Evil, and The Third Man. A couple that haven’t been mentioned are Kubrick’s The Killing (not to be confused with [) staring Sterling as a master thief with a plan to heist a racetrack. Along with [url=Bob the Gambler (1956) - IMDb]Bob le flambeur](]The Killers[/url), it’s been endlessly copied by virtually every heist movie ever made, and Quentin Tarantino essentially owes his career non-chronological schtick to this film. It has a great, ironic-noir ending, too. Also, In A Lonely Place is an often overlooked Bogart work which stands just as well as his more high profile Hammett and Chandler roles.
As for modern noir, the aforementioned L.A. Confidential is top of the heap. Farewell My Lovely, another Chandler-based film with an older, careworn Robert Mitchum standing in as Marlowe, is more or less a stock noir plot but free of the restrictions of the Production Code is a more stark and explicit adaptation of hard boiled noir. The Grifters is a sorely overlooked updating of Jim Thompson’s seminal novel for the early 'Eighties. And Blade Runner is the archtype scifi-noir film. (The true Director’s Cut is supposed to be released on DVD any day now…still waiting, Fox.)
Revisionist/parody noir: Michael Mann affects noir stylings in Heat and to a lesser extent in Thief. Scorsese’s Taxi Driver is the ugly underside of the world-weary self-styled noirish hero; one who tries to court the beautiful dame, to rescue the damsel in distress, to “wash all this scum off the streets”, except on him it looks sociopathic and desperate. Frankenheimer’s The Manchurian Candidate is part noir, part paranoid political potboiler, part Red Scare satire, and his Seconds is a social parody in the guise of a scifi-ish/noir thriller (almost more of an extended Twilight Zone.) Ronin, by the same director, has quite a bit of noirish influence in between frenetic car chases owing to the often-bleak, rain drenched cinematography of Paris and Nice, the morose, world-weary main characters (Robert DeNiro and Jean Reno), the continuous string of double crosses (and the McGuffin within a McGuffin), and the great Mamet-tuned dialog. Talking about Mamet, House of Games, The Spanish Prisoner, and Spartan all contain serious helpings of self-aware noirish affect combined with good plot twists and anacronisitic dialog.
The Man Who Wasn’t There definitely begs for someone who knows noir inside out and understands the jokes and subtle references; otherwise, it just comes off as being kind of silly. And as someone else noted, last year’s Kiss Kiss Bang Bang was a great deconstruction of hard-boiled mysteries, the fictional “Johnny Gossamer” novels that the characters keep referencing (with their interweaving, implusibly clockwork-predictable plotting) standing in for the generic dime pulp which actually parallels the story. Plus there are all sorts of mocking of conventions (ever wonder why nobody gets their fingers pinched when a character slams the door on them, or what happens when the detective playing Russian Roulette with a suspect drops the hammer on a loaded chamber), an extended joke on the pointlessness of voice-over narration, and a great scene in the end where director Shane Black basically shows you how a screenwriter sets you up for some big emotional moment and then pulls your strings. (“Did you see how he slapped that old guy around, pow, pow? That’s some harsh shit, right? Ah, whatever; anyway…”) And I love the way the chapters of the movie (one for each day) are titled after Raymond Chandler novels which presage the events to occur (“The Little Sister”, “The Lady In The Lake”, “Farewell My Lovely”, et cetera). Great film that got almost zero publicity and distribution, but well worth watching.
Check out the films of Jean-Pierre Melville (Le cercle rouge, Le doulos) and and Louis Malle’s Ascenseur pour l’échafaud if you don’t mind the subtitles. I’m also fond of the recent With A Friend Like Harry (a very Hitchcockian “wrong man” thriller), and Read My Lips, also French and neo-noirish.
Stranger
It’s a dark night on the twelfth floor of the Acme Building. In a city that knows how to keep its secrets, one man is still looking for the answers to life’s persistent questions: Guy Noir, Private Eye!
And I forgot about The Big Lebowski, which is a parody of The Big Sleep with a stoned, mostly clueless Jeff Bridges (“The Dude”) standing in for the quick-witted Bogart. Instead of being one step ahead of the (frankly unsolvable) mystery in The Big Sleep, he always seems to be about two steps behind everyone else.
Stranger