Unless you’re a fan of IFC on cable, there’s a chance you might have missed Kaaterskill Falls which I found to be surprisingly effective for a low-budget, unknown cast, indie flic.
The Dresser An acting company struggles to put on King Lear during the blitz in London in WWII. Of course the tensions between the actors are greater than the bombings.
Da, A sweet film with Martin Sheen going to Ireland to bury his father.
I’ll second The Navigator. I only saw it once back in the early 80’s and it’s still a favorite of mine.
The Tenant. Roman Polanski directs and stars in a really creepy tale.
If you are in the mood for a documentary, check out Genghis Blues.
Right on! Great movie! Pena died not too long ago. Tuvan throat singing was unknown to me before that movie. Now I hear about it in odd situations. I’d love to be able to do that. That and those Russian Bass choral groups.
Check out the Hong Kong police procedural Infernal Affairs. Not perfect, but the good definitely outweighs the bad. Also, you’ll want to see the original before the Scorsese remake comes out later this year. (Don’t bother with the two sequels, either.)
Changing gears entirely, the most completely satisfying movie I saw all last year was a tiny little film from South Korea called 3-Iron. I don’t want to say too much about it, because the less you know the better, but it’s a very simple, very quiet love story slash character study. It has a dash of the magic-realist qualities that distinguish Amelie, but it doesn’t share the same colorful-carnival sensibility. Just a wonderful, wonderful movie. Everybody I’ve recommended it to has come back to me raving.
Brainstorm. Stars Christopher Walken and Natalie Wood. This was Natalie’s last film. She drowned near the end of making it.
And The Star Chamber with Michael Douglas and Hal Holbrook.
Silverado. My favorite western.
Near Dark. My favorite vampire movie, especially because they never actually say the word “vampire.” “We’re… different…”
I don’t know how obscure this is, but Ronin is by far the best action movie I’ve seen through Netflix.
And both version of The Italian Job are worth watching.
Here’s some that sorta cover several of your genres, from great to trivial but really good to watch:
Z Great film!
The Gumball Rally. This one puts all the Burt Reynolds “Cannonball” movies to shame.
Seconding the recommendation for Outland.
Play It Again Sam. Not saying this is great cinema, put purely personally, I really, really liked this Woody Allen movie. For me, it was not only funny, but had some serious dramatic depth. YMMV.
The Professional. You got Jean Reno in what I consider his best role ever (IMHO) and a very young Natalie Portman.
I was tempted to recommend Barbarella, but won’t, since I don’t know how it would be if one watched it without being drunk or on drugs.
Without = teh suxx0rs. With = genius. 
No Such Thing is one of my favorites, yet I rarely hear people talk about it.
Red Dirt is another I like but don’t hear much about. I started a thread about it once and it got zero replies and I’m pretty sure the only views it got were mine.
Is that the one with Audrey Hepburne?
I have been suggesting *A la folie… pas du tout * (He Loves Me, He Loves Me Not) to everyone that has asked me for suggestions.
I don’t have the patience to see whether these have been recommended yet:
No Man’s Land
American Splendor
Defending Your Life
Bend It Like Beckham
Rushmore
I recently got Balzac and the Little Chinese Seamstress from Netflix - I’d read the book previously, and although there were some very slight differences, it was still very good. It is subtitled, so if that bothers you, you might want to skip it.
I agree with Omniscient’s strategy (and the strategy of the posters that followed) to look for great old films you didn’t get a chance to see when you worked in a theater.
Here’s one that hasn’t been mentioned. * The Passion of Joan of Arc* (1928).
It’s a silent, so YMMV. But it’s available at NetFlix.
If you’re looking for an excellent ghost movie, remember Shutter.
It doesn’t appear to be on Netflix yet, but it may be soon. It was made in Thailand in 2004 and is subtitled. It is very similar in palette and mood to The Ring, but is a much better movie (IMHO). Very creepy with some genuinely scary scenes, with no gore and almost no blood. Here’s hoping there’s no misguided American remake.
This movie really stayed with me!
http://www.netflix.com/MovieDisplay?trkid=73&movieid=60034047
Curdled is a great weird flick, well worth checking out.
(link double checked for accuracy) {cause I R Bad}
Here’s two really brilliant (IMO) British gangster flicks: Get Carter, (Mike Hodges, 1971) and The Long Good Friday (John Mackenzie, 1979). The former stars Michael Caine, the latter Bob Hoskins, in what may be career-best performances.
Also in the crime-detective vein, The Long Goodbye, Robert Altman’s clever update of the Raymond Chandler piece, with Elliot Gould, of all people, as Philip Marlowe; also has an amazing performance by Sterling Hayden as a drunken, bitter writer.
Westerns, any of several Anthony Mann-directed flicks from the '50’s; my personal fave is Winchester '73. For something completely different, I’d throw in Nicholas Ray’s Johnny Guitar, which is about as far out there, content- and style-wise, as any film made in a Hollywood studio in the '50’s could possibly be.
Lastly, I’ll second the previous mentions of Twelve O’Clock High, They Were Expendable, The Taking of Pelham One Two Three, The Tenant, and Z. Worthy films all. Good hunting.