Oh, great thread idea - thanks for calling me here. Hmm, 30s-50s is a very wild field, especially if there is no limit with regards to genre or nationality. There are so many great movies!
Several great movies have already been mentioned (Arsenic And Old Lace is one of my favorite comedies, The Seventh Seal is a fantastic movie that leaves you captivated, Rashomon was great and I'm a hardcore fan of Casablanca!!!). As much as I might be a film noir lover, few of them are real noir (and all are English language movies).
Sorry if most of these are insultingly obvious picks!
Off the top of my head I'd say some of my absolute favorites are:
- Casablanca (1942) (the movie to end all movies, there is even an essay by Umberto Eco on why that is)
- The Night of the Hunter (1955) (marvelous movie, very atmospheric)
- The Big Sleep (1946) (the best of them, but honestly, everything with Bogart and Bacall in it will do!!!)
- The Third Man (1949) (similar in style and also by Carol Reed: Odd Man Out (1947))
- The Man With The Golden Arm (1955) (you can hardly go wrong with Preminger and this one is surprisingly modern in thinking))
- Laura (1944) (also by Otto Preminger)
Great comedies:
- Kind Hearts and Coronets (1949) (great Ealing comedy)
- Some Like It Hot (1959)
This also the period of marvelous directors like Welles or Hitchcock (who had his golden age in the 50s, I think)
- Rear Window (1954)
- Vertigo (1958)
Great movies by Orson Welles (other than the obvious Citizen Cane, duh!):
- The Lady From Shanghai (1947)
- The Magnificent Ambersons (1942)
The Magnificent Ambersons has a beautiful intro sequence:
I'll make a more genre specific noir list...