The Coen brothers' careers as film makers reached its pinnacle in my opinion with Barton Fink, the perfect blend of humor, artistry, and symbolism. Most notably, the film won the Palme D'Or, the "best picture" of the Cannes Film Festival, in 1991.
WARNING: Many spoilers below. Do no continue reading if you haven't seen the film
My interpretation of the film is as follows: First, the movie is an allegory, telling two stories simultaneously. What occurs in one world/story, has ramifications in the other. For example, when Fink recieves the head in a box, it both causes the police to come looking for it, as well as allows him to overcome his writer's block, two things which deal with different worlds.
Fink, the main character, is a writer who feels artisticly constrained. He wants to write for the everyman, and yet, only the upper class ever see his work. He decides to go write in Hollywood. And Hollywood makes his mission impossible. It gives him writer's block. His artistic freedom is taken altogether.
The Hotel Earle represents Hell, with actor John Goodman playing Satan (notice his portrayal as a hard working simpleton gone bad, one possible perception of the Fallen Angel. Note the dusty, crumbling nature of the hotel. Chet, played by Steve Buscemi, ascends when called upon. In the elevator, the number 6 is repeated thrice (666, The Sign of the Beast). (Chihuahua_Grub makes the same observations in his interpretation). Fink is unaware of how to progress in his art in this stifling world. He cannot simultaneously write a wrestling picture to Hollywood's parameters and a wrestling picture which represents the ideals and struggles of the everyman. He needs help. He needs, frankly, a Muse.
That Muse is Audrey Taylor, played by Judy Davis. Notice that after his first novel, W.P. Mayhew has Audrey write all his novels. She is creativity and style, and all of Fink's wildest writing fantasies. So, they sleep together. This isn't enough. Fink needs the Muse all to himself to survive in Hollywood. Fink then sells his soul to the Devil, in exchange for the Muse's head, which is given to Fink in a little brown box. In the real world, this selling of the soul is represented as contractual bondage with his film studio. Fink can now write, but no one, not even the upper class, will ever see his work. And suddenly, Barton Fink can write to his hearts content. He has found some level of happiness (the woman on the beach).
Also apparent are undertones of sexual frustration. Barton Fink cannot write, perhaps because of his lack of sexual activity. Whenever he attempts to write, he always ends up simply staring at the picture of the woman on the beach. Finally, Satan arrives promising beautiful women (the picture of the girl on his tie). In the end, he delivers Audrey Taylor.
If you enjoyed this film, I also recommend The Hudsucker Proxy and Raising Arizona of the brothers' other works, along with the films Mulholland Dr. and Lost Highway by director David Lynch and Jacob's Ladder, directed by Adrian Lyne and written by Bruce Joel Rubin.