Ahh right now im in my Japanese 1950s movies phase. so I would go for:
Tokyo Story (Ozu)
http://imdb.com/title/tt0046438/Ikiru (Kurosawa)
http://imdb.com/title/tt0044741/Floating Weeds (Ozu)
http://imdb.com/title/tt0053390/Theres still a lot of kurosawa films i havent touched, but thank god for Netflix, I'll be able to watch all of them.
Theres this korean movie called "The Way Home(Jibuero)" which is about the relationship of an old Grandmother and a spoiled Grandson, which by the way made me crying like a broken dam.
http://imdb.com/title/tt0312841/Also another korean movie is "Oasis" which is about a peculiar love relationship between a 20+ woman who is cerebral palsy and a 30+ yr old mentally challenged man. This movie is about barriers(communication barriers). A must see film.
http://imdb.com/title/tt0320193/ Also another japanese movie I watched recently which should be given time for viewing is
"Nobody Knows." Which I think is one of the most beautiful sad movies of all time.
http://imdb.com/title/tt0408664/ Best anime movie should be given to AKIRA. That movie is way way ahead of its time. in every degree, as far as storytelling, soundtrack, visuals philosophical values etc. goes. it came out 87? or 88?
http://imdb.com/title/tt0094625/On a side note, just saw this 70s move called "Colossus: the forbin project" which is one of the first Artifical Intellegence themed movies, and I tell you this movie is very very creepy. Though the ideas of the movie have been cliched in almost every AI movies, This one pioneered all of them.
http://imdb.com/title/tt0064177/Though these movies arent "the greatest" it is a must see for everyone. A truely life changing experience.