This is a deliberately unconventional pick. Orson Welles directed many other films that fit better into the noir canon - The Stranger, The Lady from Shanghai, and the film noir to end all films noir (literally), Touch of Evil - but The Trial is a newfound favorite of mine.
I'm not going go into too much detail with it, because discussing enough details to give the movie justice would quickly expand this post into book-length. But The Trial is a cinematic adaptation of Franz Kafka's novel, turned by Welles into a sharply stylistic, brutally beautiful dream of oppression and death. In a very loose sense, it's very noir-like in its themes (complete with some mysteriously dangerous dames). It's almost a meta-noir. It's also essential for any noir fan to watch, if only to compare to the other, more conventional offerings.