I've just watched Rust and Bone which came out at the cinema last year-thoroughly enjoyed it-quite gritty and very moving at the end. About a women who loses her legs in a whale accident and a bare knuckle fighter single parent!
The Edukators (you'll like if you liked Goodbye Lenin)
Joyeux Noel (about the Christmas truce 1914)
Night on Earth (early Jarmusch, 5 taxi rides in 5 cities of the US/Europe)
No Man's Land (a bit grim, Bosnian war)
My off the wall suggestion: 9th Company, it's one of the biggest Russian films ever made, about the Afghan war. It's the Russian version of Full Metal Jacket, basically. It's pretty insane but really interesting.
We love asian cinema in particular. Anything by Studio Ghibli (a japanese animation studio roughly on a par with Disney -but much better in our humble opinion) is gold, not just for children but for adults too. My Neighbour Totoro, Laputa : Castle In The Sky, Spirited Away (which got an Oscar), Kiki's Delivery Service, Ponyo On A Cliff By The Sea. All good!
Otherwise, well it's boring to list but also more succient. Gotta love:-
Most stuff by Park Chan-Wook (he is South Korean and his Hollywood debut 'Stoker' is out this week) including Oldboy and Joint Security Area.
Chow Yun-Fat has been in some great films like Crouching Tiger, Hidden Dragon and A Better Tomorrow.
Twins Effect (Hong Kong weird comedy / horror vampire film) Ring (Japanese original) Election (Chinese Trid film).
Non asian greats:-
Cinema Paradiso (already mentioned) District 13 (French free running film) Amelie (already mentioned - gorgeous) Also Life Is Beautiful (Italian - film about the persecution of Jews in WWII. Suprisingly funny but heartbreaking ending)