Best Classic Movies About Prostitution?

The tawdry, pre-code BABY FACE (1933) has Barbara Stanwyck being prostituted by her father, then she moves to the big city to "use men to get the things she wants."

SEE: http://youtu.be/_NkcRllnmFo

Irma La Douce or is that too modern?

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Both of Louise Brooks's famous movies w/ Pabst, Pandora's Box and Diary of A Lost Girl, have her as a prostitute (at least some of the time).
Marlene Dietrich is the most exalted/notorious prostitute in China, 'Shanghai Lily', in Shanghai Express (1932).
Both Waterloo Bridge's (1930, 1941 IIRC) have an important supporting character who has to be saved from prostitution.
Bresson's early masterpiece, Les Dames du Bois de Boulogne, has a fiendish revenge plot about fooling an ex into unknowingly marrying a (former) prostitute.
Several Ophuls films, e.g., La Ronde and Le Plaisir have major prostitution sub-plots.
Nights of Cabiria has already been mentioned
Anna Magnani is a salt-of-the-earth ex-Prostitute whose past costs her her son in Pasolini's Mama Roma (1962)
Godard's Vivre sa vie has already been mentioned.
Janet Munro is a classic 'falling into prostitution and drugs' cautionary tale in Bitter Harvest (1963)
Catherine Deneuve is a bored rich woman who works at a brothel during the day for kinky kicks in Bunuel's Belle de jour (1967).

All of these films are very good to excellent.

Leaving Las Vegas

Night Shift!

Breakfast at Tiffanys

Yes to Klute!