A sort-of "Noir for Dummies" post by movie critic Roger Ebert can be found here, via. I'm not an expert on the "Film Noir" style of movies, but here are some links to lists, articles, and movie trailers and clips (w/some complete movies).
A "Top 50" list of "Film Noir" movies (as voted on by people that visit their site) can be found at imdb.com here, with a more complete list of 500 movies over here. I'm a little dubious that there are that many "Noir" type movies out there (Does anyone really think "The Ox-Bow Incident" is Film Noir?), probably a lot of crime and gangster or more recent titles thrown in there.
Tons of great research on film noir from origins of noir through modern explorations of the style can be found on filmsite.com, the last page has lists of "Classic Film Noir" (40s and 50s) and "Modern Film Noir" (1960-2006). This site is somehow attached to American Movie Classics network and it's affiliated channels and websites. Check out page one, two, three, four, five, and six.
Anyone looking for full-length "Film Noir" movies probably already has a cozy setup tailored to their computer already, however here are some places to look for us just starting the hunt:
=Retrovision.tv has these movies under the film noir-heading (I believe these are permalinks to other sites??): Amazing Mr. X, The (The Spiritualist); Beat the Devil; D.O.A.; Daughter of Horror (Dementia); Detour; Fear in the Night; He Walked By Night; Hitchhiker, The; Impact; Inner Sanctum; Jigsaw; Kansas City Confidential; Panic in the Streets; Parole Inc.; Payoff, The; Phantom of 42nd Street, The; Red House, The; Scar, The (Hollow Triumph); Scarlet Street; Second Woman, The; Strange Love of Martha Ivers; T-Men; Too Late for Tears.
=http://www.archive.org/search.php?query=collection%3Afilm_Noir&sort=-publicdate has 43 titles under the heading film noir. I tested this site out, and was able to download in MPEG2 "Too Late For Tears" (w/the awesome Lizbeth Scott and Dan Duryea) to my Windows Media Player for no charge or registration.
=Veoh has a few movies tagged as "Film Noir" (and about as many old crime movies): The Big Combo; The Dark Hour; Detour; Killer Bait (Too Late For Tears); Money Madness; Port of New York; The Scar (Hollow Triumph); The Steel Trap; Sunset Boulevard; Woman on the Run.
=The biggest site if you're just looking for clips or trailers is definitely tcm.com website of Turner Classic Movies channel. Here's a list of some "Film Noir" (maybe a couple that aren't exactly, my fault not their's) movies with a link to their database page on the site: Ace in the Hole, Angels With Dirty Faces, Asphalt Jungle, Beware, My Lovely, Beyond a Reasonable Doubt, Big Clock, Big Heat, Big Sleep, Blue Dahlia, Body and Soul, Boomerang, Brute Force, Cornered, Crack-Up, Criss Cross, Crossfire, Dark Corner, Dark Passage, Double Indemnity, Force of Evil, Gilda, Glass Key, He Walked By Night, High Sierra, Human Desire, I Am A Fuguitive From A Chain Gang, In a Lonely Place, Intruder in the Dust, Johnny Angel, Key Largo, Killer's Kiss, Kiss Me Deadly, Lady From Shanghai, Lady in the Lake, The Las Vegas Story, Macao, The Maltese Falcon, Miami Expose, Mildred Pierce, Ministry of Fear, Murder My Sweet, Naked City, Narrow Margin, Niagara, Nightfall, Night of the Hunter, On Dangerous Ground, Out of the Past, Pickup on South Street, The Postman Always Rings Twice, Railroaded, Shadow of a Doubt, Sorry Wrong Number, Sunset Boulevard, Sweet Smell of Success, They Live By Night, The Third Man, Touch of Evil, Violent Saturday, White Heat, The Wrong Man.
noiroftheweek.com looks like a well-done fan site for "Film Noir" movies, check here for a complete list of movies they've reviewed.
"Double Indemnity" clip from YouTube, a very sexy scene that is pretty much the epitomy of the sex side of the "Film Noir" style.
"Nightmare Alley" clip also from YouTube, this is the flipside of "Film Noir" the downfall of the hustler at the hands of a woman (or two, in this case).