In spite of this blatant complexity, film writers and thinkers want to pin a movie on one person. Why do we care for such reduction? As human beings, we are inclined to tell stories and to reduce other disciplines to stories. Stories need a protagonist. Singular protagonists are more relatable and provide a focal point that mass protagonists do not. Directors, or sometimes someone else, are seen as the "great men" of film history. Reducing a movie to the work of a single man also makes it easier to talk about movies for those who don't understand the technical side as well or at least weren't privy to the goings-on on an individual production.
As most productions are too complex to truly be reduced to one person, I will examine the major roles and how they might be the most important. Is it the producer, the director, the writer, an actor, the cinematographer, or the editor? I sometimes like to believe it's the grip. My very limited viewpoint on the subject is partially based on general knowledge and partially based on my own on-set experiences. These roles are, of course, fluid, and no two productions are exactly the same.
The producer does a lot to bring a movie together in pre-production. He may well be pitching it to different investors. He'll manage many of the pieces including budget and scheduling. It is often seen as his most important creative role to hire the director.
I would usually consider the director the most important creative force if I had to choose. The director is pretty much the only person working with the actors on a set and channeling their performance. While other people toil away on set, the director has final say on just about everything. The notion of director as author of a film was popularized in the 1950s with the auteur theory coming from folks like Francois Truffaut and others in France and later Andrew Sarris was a prominent promoter of it in the U.S. The notion was that you could see the imprint of a singular director over the course of his body of work, apparently in a way not found with other roles. This approach has made big names out of people like Orson Welles, Alfred Hitchcock, and John Ford here at home, and Jean Renoir, Vittorio DeSica and Akira Kurosawa abroad.
It's interesting how Americans relate to movie writers. When we talk about movies, we almost entirely talk about story. Mainstream film making is generally designed to make us focus on story and leave the other elements "invisible." Despite our emphasis on story when we focus on the people making movies, we tend to celebrate directors and ignore screenwriters, sometimes to the point of imputing screenwriter elements to a director. Mainstream movies are usually relatively formulaic in terms of script, but a lot of variation has been made within the formula found in basic screenwriting books, and other elements are relatively formulaic, too.
Actors are probably the most recognizable role for the layman. They are the ones in front of the camera and we see the product of their labor in a more overt way than the rest of the people working on a production. Actors have contributed some of the cinema's most iconic elements in great performances such as Charlie Chaplin in The Gold Rush, Marlon Brando in On the Waterfront or Amitabh Bachchan in Sholay. Actors, though, mainly just control the small piece of the movie that is them and owe at least part of their performance to a director. Even film history's most iconic performances were generally tied to a famous director.
The cinematographer supervises the lighting and shooting of a movie and thus has a hand in very single shot of a movie. While the director must ultimately okay the cinematographer's choices, he can only choose from what is set in front of him and on a healthy, functioning set, he shouldn't have a strong habit of saying no. The two should be working together. How much influence each has is variable to any set, but the cinematographer is certainly an important role.
The editor is very much an unsung role. The editor has a lot of power to shape the final footage with what was shot. He finishes the movie, in a way. On the other hand, editors generally work in concert with directors and have to have their work okayed first by the director and later by the studio, investors, etc. This is why we sometimes here about a director's cut but never an editor's cut.
This entire discussion reminds me of one of my all-time favorite movies, Into Great Silence. It's an impressive direct cinema documentary about the Carthusian monks who have taken a vow of silence. The same man shot and edited with no outside input, quite a feat for a feature documentary that somehow works, in my opinion, despite virtually no narrative line.