Good question - it's not easy to answer, and certainly changes from director to director (as it does country to country, and year to year).

The director is the creative drive behind a film, the final funnel through which all other individual aesthetic responsibilities are filtered; the director is responsible for communicating his vision to the experts in their particular field - costume design, editing film together, lighting, etc.

Jay Rabinowitz is credited with "film editing" on Requeim. What this means is the technicality of splicing together reels of film, but also the overall rhythm of a narrative (what goes where), which involves the inclusion and omission of scenes and shots. He'll be guided by Aronofsky, who, as director, is responsible for communicating what he wants to those around him.

Martin Scorsese and regular editor Thelma Schoonmaker are a good example of a director/editor partnership; they'll both know, by now, how the other works - Thelma will know what Marty wants, Marty will trust Thelma to best get his vision across.

It isn't just editing that this applies to. Cinematographers, too, who are doubly responsible for a) listening to how the director thinks it best to shoot the film (and putting their own input in as required), and b) choosing the right lighting system to make that happen; oh, and c) communicating what the director wants to the people operating the actual cameras (if it isn't the cinematographer him/herself).

Some directors like to do everything themselves - writing, directing, shooting, editing, even writing the musical score for the film (Charlie Chaplin, for the most part, was like this). Others will fully embrace the collaborative nature of filmmaking and somehow still get their authorship stamp into the work (Hitchcock, anyone?).

EDIT: Also, I think it's interesting to note that more and more films are being shot on cheaper material now, with the move toward digital and away from actual celluloid. Film stock is expensive, and very difficult to develop and expose just right; but now that DV and HD are much cheaper, filmmakers are able to film with a lot more flexibility. In some ways, it might be argued that there's a trend now that hints at the emergence of the editor and the dampening of the cinematographer... for certain sorts of films, anyway.

But I think the holy trinity for a great film comprises of the director, the editor and the cinematographer.

(The producer, for me, lies outside the creative bounds of a film; he's more of the financial spearhead.)