Some directors that haven't been posted yet:

Majid Majidi (Iran) - "The Color of Paradise" or "Children of Heaven".  Both are universally accessible films that are good primers to Iranian cinema.
Jafar Panahi (Iran) - "The White Balloon".  Good introduction, not only to Iranian cinema, but also Abbas Kiarostami's 'real-time' style (he wrote the screenplay).
Dairush Mehrjui (Iran) - "Leila".  Excellent look at the conflict between cultural tradition and modern society when a young couple is unable to have a child.
Youssef Chahine (Egypt) - "Aexandria Trilogy:  Alexandria, Why?, An Egyptian Story, Alexandria:  Now and Forever".  Great nostalgic examination on the often turbulent history of Egypt.