I've just checked Netflix and all of these are available so here's a little sampler.
Comedy:
Triplets of Belleville This is a cartoon and though it's French, there's actually very little diaglogue. It's about a skinny cyclist who is kidnapped, three elderly caberet singers who have an unusual way of finding their dinners, and a short, stout mother who loves her son.
Belle Epoque A Spanish film featuring a very young Penelope Cruz. Three sisters fall for a handsome Spanish soldier returning home from war, but who gets him? It's not half as funny or charming if you see it dubbed; suffer through the Spanish and you'll be glad you did.
The Closet A French film about a homosexual who's not a homosexual with a sex-on-the-table scene that will make you split a gut laughing.
Romance:
Les Enfants du Paradis A black-and-white French film set in Paris, about a mime who loves a beautiful actress who is also loved by other men. You have to be devoted to old films to sit through this one because it moves slowly--it's more about atmosphere and nuance than anything else, but your heart will break as you follow the mime's eyes as he gazes upon his beloved.
Il Postino An Italian film worth looking at for the scenery alone, but luckily a very good movie! The postman speaks the words of a poet to snare his lady love.
War
Das Boot Life inside a German U boat during WWII makes for a movie that is chilling and claustrophobic; must be watched in the German.
La Vita e Bella Robert Begnigni plays a Jew married to a Gentile during WWII. He is thrown into a concentration camp and lives a charade for the sake of his young son. It ought to be deathly depressing and draining but Begnigni plays his part with such lightness and grace that you see through the eyes of the boy, and it is a happy film in that sense, as Benigni's character intended.
Nowhere in Africa A European man and wife leave their comfortable life behind as they flee to Africa at the advent of WWII. The film's long but it's a fascinating look at displaced people and how they adapt--or not.
Epic
Indochine One of my all-time favorite films ever. It stars Catherine Deneuve as the wealthy, cultured owner of a rubber plantation in French Indochina as war breaks out. Her adopted daughter falls for a beautiful young man not knowing that he is her mother's lover. This film has it all--political intrigue, a country in crisis admist a changing way of life, a raw look into the harsh class system during colonial days, incredible scenery and more.
Music
Diva A young messenger boy in Paris is in love with an opera singer and also unwittingly involved in a prostitution ring when an incriminating taped confession falls into the bag of his delivery bike. The same bag that has a secretly taped concert of the opera diva. Two sets of criminals want what he has. The film is very stylized and it's hard to believe it's more than 20 years old now.
I have more foreign films up my sleeve if you're interested, but it's time to

now.