If none of the above are your favorite, then please name your favorite director and also briefly (or not briefly) explain your choice. Some people may be irritated that Steven Spielberg is among the choices, but many influential (and arguably superior) directors such as Eisenstein, Lynch, Fellini etc. are not. The reason for this is simple: this poll is about who our favorites are and not about who we think is the most critically acclaimed or important director of all time, even though the two may very well be one person for some voters.
So as to not be indifferent to my own topic, my favorite film director of all time is Ingmar Bergman. I don't think he was the best at setting up great looking shots (Welles and Kubrick have him beat at that), but I love him more than any other director because of what his films are about. Bergman usually wrote his own scripts, something that lead Kubrick to state that Bergman was one of only three directors (the other two being Fellini and De Sica ) who wasn't just an artistic opportunist, waiting for a good story to fall into his lap. Bergman's films deal with many of the biggest problems that have intrigued mankind (probably) ever since we became capable of conceptual thought. Problems such as the existence/ non-existence of God(s), the human condition and the fear of the inevitability of death, self-discovery and many others. What makes his films work so well for me is the way that he expresses different points of view through different characters, which often leaves me wondering which character Bergman himself most identified/agreed with, if any. Bergman's stories are incredibly beautiful, often dark, they feature great characters and the dialogue feels 100% authentic and never makes one feel as if it is coming from a script (often it isn't, because he let his actors improvise a lot).
If I had to pick a favorite of his films then it would be his best known work "The Seventh Seal". You probably wouldn't believe that a film that has death as it's major theme (along with other favorite themes of Bergman's such as the silence of God, betrayal, insanity etc.) could produce so many laughs, but it does. It is a genuinely funny film, while also being very thought-provoking, emotionally and intellectually involving. You probably also would not believe that a black and white film could be the most beautiful film ever made, but it is. There's only one way to become a believer and that is too see it, I recommend that you do. It is a masterpiece.

Runners up in my favorites list (no particular order): David Lynch, Peter Jackson, Baz Luhrmann, Orson Welles, Terry Gilliam, Martin Scorsese.