Many great films so far mentioned but would like to add "Ascenseur Pour L'Echafaud (Lift To The Scaffold) with Jeanne Moreau and a magnificent music soundtrack by a group led by Miles Davis.
I remember the days when it was possible to regularly see such films at cinemas in Brighton. The two being the Continental in Kemp Town and the Paris in New Road.
The down side was that in those days if people knew you were a patron you were usually considered to be someone going to hard porn...