I haven't seen this topic on here before, and it seems a worthy subject of discussion.  So, here goes.  (Note that I'm not going to keep anything off my list since it might show up on everyone else's.)

Greed
Sunrise
Scarface (Hawks)
The Shop around the Corner
The Magnificent Ambersons
Scarlet Street
Monsieur Verdoux
The Night of the Hunter
2001 (Is it really American?  Close enough, I say.)
Martin (Romero)

That's just dashed off in the heat of the moment.  I'll think about this more and come back later, perhaps adding a few runners-up.