Firstly, everything roadie said is to be trusted... I can definitely recommend most of what he mentioned, and am actually looking at the cases for a number of them right now. That said, here's a breakdown of some stuff you can find relatively easily (and never take video culture for granted, that place is probably the best video store in the 7 states visible from Rock City).
For French cinema, Godard's Breathless is my favorite and a great place to start for "New Wave" stuff. If liked, Truffaut's 400 Blows and Godard's Band of Outsiders are excellent as well. If you want to get really out there, Godard's Weekend and Masculin/Feminin are fantastic, if not highly alienating to most people.
Also French, but very different, is Renoir's Rules of the Game. Hard to find, this social satire is brilliantly funny yet touching and poignant. You'll laugh til you cry, then cry because you shouldn't have laughed. Well, it isn't really that serious, but this is one that plays all strings.
For Italy, Fellini is indispensible. I make no bones about 8 1/2 being my favorite film of all time, and there's alot to be said for the rest of his early work, La Strada, La Dolce Vita, and Nights of Cabiria in particular. His later work is rather hit or miss, but Amarcord is an example of a hit. Alos from Italy are the neorealist directors, and Vittorio De Sica's Bicycle Thieves is probably the best place to go for that.
The recent "new" Latin American cinema is extremely rich, and exciting, and highly accessable to modern american audiences. Already on DVD are Amorres Perros and Y Tu Mama Tambien, and City of God (which stopforme mentioned) should be coming to video this year. All are fantastic.
My favorite foreign director is probably Akira Kurosawa, and really all of the Criterion collection Kurosawa films are great. See Rashomon, Seven Samurai, Hidden Fortress, Yojimbo, and Ran first, though really nearly anything of his is a safe bet. He's of interest because the Eastwood Westerns and Star Wars films are direct rips of his work. All around solid stuff.
The recent release of Kieslowski's Three Colors Trilogy has been the most exciting thing to come out this year, as far as I'm concerned, and Kieslowski's Decalogue is coming to dvd this month (after having been out of print for about a year). The three colors trilogy is about as good as cinema gets, in my opinion.
Wong Kar-Wai's hong kong cinema is very different from John Woo's (which is worth exploring, but I won't go in to), and in my opinion, better. Chungking Express is great for those who liked Amelie, I've got a friend convinced that Amelie is nothing more than a rip of Chungking's second half. I Won't go that far, but Chungking is the kind of film that just excites me watching it. One of my favorites. Also from Kar-Wai is In the Mood for Love, a slow but rich look at relationships.
Luis Bunel's films are always a ton of fun, if not hard to find. Criterion's got a good disc for Discreet Charm of the Bourgeoisie though, and it is a favorite of mine. He worked, early on, with Salvador Dali, and so that gives you an idea of his sensibilities. Discreet Charm is filled with a multitude of random, fun episodes, loosely linked by the thread of wealthy people wasting time and money. A ton of fun.
Almondovar's Spanish films are the only Spanish film that I'm very familiar with, but Talk to Her and All About my Mother are both fantastic.
Ingmar Bergman is an amazing director who often accomplishes the feat of having films that are slow and feel like they are taking 4 hours, yet after 90 minutes are done, yet feel like they had 8 hours of content. And odd description, perhaps, but that's how I feel. They are very weighty films, though, and only appropriate if you want to put some thought into it afterwards.
German film is not to be ignored. You have probably seen Tom Tykwer's Run Lola Run. If not, do. Its is a great, exciting film that used the aesthetic of music video and video games to tell its story. Good stuff.
As for the rest of German film, the three big German new wave directors are Herzog, Fassbinder, and Wenders. For Wenders, Paris, Texas or Wings of Desire would be most recommended, especially the new dvd of Wings of Desire, which my friend contends is the most beautiful film ever. Herzog is good if you like insanity, in which case, Even Dwarves Started Small is the most insane. Aguirre, the Wraith of God and Fitzcarroldo are also about insanity in some way and are great movies, and both easier to watch perhaps than Dwarves, which is pure chaos (and in my opinion more fun for it). Fassbinder is my favorite of the three, and of his work, I most recommend Fox and His Friends, The Marriage of Maria Braun, Merchant of the Four Seasons, Ali: Fear Eats the Soul, and Why Does Herr R. Run Amok? All of these are more serious than the Herzog, but all excellent films.
Wrapping up, looking at my shelf I see a few films that aren't foreign-language but which probably wouldn't be seen otherwise and really ought to be. Of those Brief Encounter (directed by David Lean before he went on to Bridge on the River Kwai and Lawrence of Arabia) and George Washington are the best. Brief Encounter is a small, 90 minute film about an affair that is overly melodramatic, but always strikes a chord with me despite this fact. Just solid filmmaking all around. George Washington is rather new, and one of the few films I know of that depicts the South acurately without being overly kind or overly cruel.
To round this out, the list of my most recommended films would be:
1. 8 1/2 (Fellini, Italy, 1963)
2. Rashomon (Kurosawa, Japan, 1950)
3. Rules of the Game (Renoir, France, 1939)
4. Breathless (Godard, France, 1960)
5. Three Colors Trilogy (Kieslowski, Poland, 1993)
6. The Seven Samurai (Kurosawa, Japan, 1954)
7. Chungking Express (Wong, Hong Kong, 1994)
8. Brief Encounter (Lean, Britain, 1946)
9. Amores Perros (Innaritu, Mexico, 2001)
10. The Discreet Charm of the Bourgeoisie (Bunuel, France/Spain, 1972)
Hope you see some of these, they are great.
Will
You may like grandma's yard gnomes, but I've seen Rock City. Remember it.