Your reader poll winner is a high-flying martial arts extravaganza that I think was the first subtitled movie I (and lots of other people) saw in a theater.
A French masterpiece about upper-class romantic games, played blithely as the world teeters on disaster.
The story of women trapped and exploited in a gilded cage, the first film by a female director to come out of the Arab World.
A small, emotional film from Communist Hungary about the unlikely friendship between two women from different worlds.
The first film from Sub-Saharan Africa to make a big splash in Europe and the US, its story about the toll of colonization is very relevant even today.
A rural village in the Philippines is dragged into the modern world when a local girl claims to see a vision of the Virgin Mary.
A lot more people know the idea of it than have actually seen it, but it really is worth watching.
Maybe the first feature film dealing with themes of homosexuality, it feels surprisingly fresh today.