Alright:
- I second kowen, and I do recommend The Big Lebowski, Jeff Bridges is awesome, and Steve Buscemi and John Goodman have great parts in that movie. I'll add Intoreable Cruelty and Burn After reading. Oh, and True Grit (again Jeff Bridges), and O Brother where art thou are also rather good.
- Yeah, Kurosawa. But, try a trailer first, I've watched Yojimbo, and Seven Samurais, great movies they can be too slow for some people. If you are into Hollywood fast paced starndars, you may want to skip those. You'll be missing some great movies tho.
- Great recommendation from pauluzzz1981, Das leben der anderen, amazing movie.
- As many have said, pretty much anything from Ghibli, and as KingWithNoKrown if you are into anime Princess Mononoke is a must. Ohtomo's Akira, and Steamboy are also recommended, and Metropolis (the German Classic is also recommended, but again, a slow movie).
- I didn't like The Fracture, it was ... meh.
Now my personal suggestions. Michel Gondry's The science of sleep is one of my personal favourites. Be Kind Rewind, and The Eternal sunshine of the spotless mind, are not bad either.
Fatih Akin's Soul Kitchen is a superb comedy.
You may also want to check Shaolin Soccer and Kun-fu Hustle from Stephen Chow, but I've been told that his older stuff is much funnier.
Uhm and also, from Tomas Alfredson Let the right one in (there is also a hollywood remake), and Tinker Taylor Soldier Spy.
I could keep going but, well, thats the first stuff that came up in my mind.
