i was about to ask a similar question-though there's always the difficulty in separating the personal/subjective,i.e."favourites",from the objective.,i.e "greatest".
Anyway,my own favourites are:
MIZOGUCHI,Renoir,Tarkovsky(pleasantly surprised to see so many of you rate him),Hitchcock,Kubrick,early Wenders(his later work has been a terrible disappointment).To a lesser extent, Rohmer,Ophuls.... I 've greatly admired those Angelopoulos films i've seen.
Of course,  Kurosawa,Bergman,Fellini,Welles,Godard,Bunuel,Kiarostami,Kieslowski,Dreyer,Bresson,Eisenstein and Ozu have been important and still greatly admired by many.And Murnau, for Sunrise especially, also Nosferatu.(Silent films aren't seen enough by the public, should be more accessible internationally).Of British directors,Michael Powell is surely the best,though i know Lean has many American admirers.The critical esteem of De Sica, Chaplin,Griffith has faded,i think.Truffaut has been rather overrated,in my opinion.I'm not at all enamoured of Spielberg, but if you're judging "greatest" by commercial success(i hope not!)...
Important directors from relatively neglected areas include;Ray,Sembene,Chahine,Dutt,Ghatak.Indian Cinema is only now receiving close attention,and Africa and Latin America still await proper recognition;the international consensus and "canon" of greats will evolve...