There are a great many good non-american movies. Here are a few I would consider classics and their country of origin:
Sånger från andra våningen(Songs from the Second Floor) - Swedish film, very surreal but quite interesting. Consists of a series of tableaus and does not really have a general story, but manages to convey a sense of despair and disillusionment in a modern society very well. It's also quite funny on occasions.
http://www.imdb.com/title/tt0120263/
Funny Games - A German movie despite the title. Instructed by Michael Haneke. This is possibly the most creepy movie I have ever seen, which is just a testament to how well it is done. It manages to be so extremely nasty without even being particularly visual in its violence, and the director constantly toys with the viewer, plays on his expectations and turns them upside down. This is anything but an uplifting movie, and it is not one to choose if one simply seeks Friday night entertainment, but it is definetely one to watch. An American version is scheduled to come out this year, but I would recommend checking out the German original anyway. I doubt they can find another actor who'll do the part of Paul half as well.
http://www.imdb.com/title/tt0119167/
Der Siebente Continent(The Seventh Continent) - also German, also Haneke. This one I found even more disturbing than Funny Games. It is a very dark movie about a modern disillusioned family, and the way they eventually seek to escape the coldness and triviality of their current existence. It is amazingly well done, however, so it is certainly worth watching, even with the shocking effect it can have on the viewer(when I saw it with a bunch of others for the first time, we all just sat for a minute in stunned silence when the movie had ended, none of us speaking a word.)
http://www.imdb.com/title/tt0098327/
Festen(The Party) - A Danish movie which has received quite a bit of international acclaim. It is also somewhat nasty, it tells the story of a birthday party during which very dark revelations about a family's past are made. The interesting thing to watch is how everyone strives to make the party go on even as the horrifying reality of the past events start to dawn on the guests.
http://www.imdb.com/title/tt0154420/