Film Noir suggestions

the third man
touch of evil
the asphalt jungle
city that never sleeps
the big heat
white heat
night and the city
body and soul
out of the past
nightmare alley
the desperate hours
sweet smell of success
key largo
in a lonely place
laura
double indemnity
witness for the prosecution
strangers on a train

The Window (1949) In one article I read about this film, it was supposedly the inspiration for Hitchcock's Rear Window a few years later.

Pushover (1954) features a 21 year old Kim Novak in her first starring role.

Panic in the Streets (1950) features Jack Palance in his film debut.

Highway Dragnet (1954) B Grade but compelling and a little different.
Inferno (1953)
Day of the Outlaw (1959) a Western but has a Film Noir feel to it.
Crossfire (1947)
Criss Cross (1949)
In a Lonely Place (1950)

If you wanted to try something newer The Last Seduction (1994) has all the hallmarks of a Film Noir too.

Some of my favourites that haven't been mentioned yet:

Born to Kill (1947)
Detour (1945)
Each Dawn I Die (1939)
Gilda (1946)
The Killers (1946)
The Killing (1956)
Kiss Me Deadly (1955)
The Lady Vanishes (1938)
Mildred Pierce (1945)
My Name Is Julia Ross (1945)
The Narrow Margin (1952)
The Night of the Hunter (1955)
Suddenly (1954)
Sunset Boulevard (1950)
They Live by Night (1948)
Where the Sidewalk Ends (1950)

Ace in The Hole
The Blue Dahlia
Sunset Boulevard
Chinatown

The Element of Crime (1984)
Dark City (1998) - Bonus: a SUPER hot Jennifer Connelly