For me, it's far more challenging to try and pick the Greatest Directors in terms of importance and influence.

This is my semi-educated guess:

1) D.W. Griffith 
2) Sergei Eisenstein (Over Pudovkin, Vertov or Kuleshov.)
3) Robert Flaherty (Over Leni Riefenstahl)
4) Luis Buñuel
5) Jean Renoir
6) Fritz Lang (Over F.W. Murnau)
7) Roberto Rossellini (Over Vittorio De Sica)
8) Akira Kurosawa
9) Jean-Luc Godard
10) John Cassavetes

This was incredibly difficult, and my list is not very good. It more or less embodies people who were at the forefront of some of film's most important movements. The one that I'm least happy with is Jean Renoir, because I'm not convinced he's the embodiment of the Golden Age of French cinema. I chose him because he had an incredible influence on cinema around the world, and still does today. I wanted to include John Ford, but in the end, I decided he was more of a continuation of Griffith, whereas Cassavetes is the father of independent American filmmaking. 

I considered including Hou Hsiao-Hsien, but my knowledge of "Chinese" cinema before the 80's is terrible, and I'm sure there's someone more influential or important. I also haven't included anyone from Indian cinema, which is pretty unforgivable. But there you have it!
