Click here to read David Haglund's essay on watching all of the Coen brothers' movies.
There is more to Coen brothers completism than the 15 feature films Joel and Ethan have written, produced, directed, and edited. There's Crimewave(1985), for instance, the movie they wrote with Sam Raimi that he directed. It's noticeably a Coen brothers movie: A nerdy nebbish gets in the way of two scary if bumbling criminals carrying out a businessman's evil scheme. Raimi amps up the creepiness (and the cartoonishness; he also co-wrote The Hudsucker Proxy). I'll leave it for Raimi fans to defend that one.
The Coens have also made two short films, both of them available on YouTube. "Tuileries" is the longer (and more expensively produced, I'm guessing) of the two. It stars Steve Buscemi as an American tourist who, at the Tuileries metro stop, endures several of the ignominies an American might predictably fear from the French. It's part of the omnibus film Paris, Je T'Aime(2006), though the Coens seem to have no love for the place.
Their other contribution to a French omnibus film is both more casual and more charming. "World Cinema" was made for Chacun son cinéma, commissioned for the 60th anniversary of the Cannes Film Festival. It features Josh Brolin as some kind of cross between his Llewelyn Moss from No Country for Old Men and his George W. Bush from Oliver Stone's W. He walks into a movie theater and asks the ticket seller (Grant Heslov) for help choosing between Nuri Bilge Ceylan's Climates and Jean Renoir's The Rules of the Game. Though he arrives wondering if either film has nudity or livestock, he leaves, after watching Climates, saying the movie had a "helluva lot of truth in it."
Also worth seeking out is the Coens' larger-than-one-might-expect body of advertising work. You may have heard about their "clean coal" spot from 2009, which, like much of the Coens' work, tweaks the conventions of a familiar genre—in this case, the cleaning product commercial—to darkly comic effect. But the golden age of Coen brothers advertising was in the late '90s and early '00s, and seems to have begun with their work for Honda: According to the New York Times, they produced several spots devoted to the Odyssey and the Accord, though only one of them appears to be available on YouTube. It bears a family resemblance to The Hudsucker Proxy—as does the Coens' 2002 spot for H&R Block, which aired during Super Bowl XXXVI.
Better than both of those commercials, in my opinion, is the Coens' brief, wordless advertisement for white button-downs from the Gap, in which their camera simply pulls back on a poolside chess match between Christina Ricci and Dennis Hopper to the strains of "Hang On to Your Ego" by the Beach Boys (another version uses "I See the Rain" by the Marmalade). To sell a very simple product, the Coens distill the ingredients of summer advertising into a single composition: the curvy pool and round table elegantly juxtaposed against the right-angled chairs and chess board, Ricci's arm aligning exactly with the top of the pool as she hands Hopper his lemonade. (The ad campaign also featured spots by Cameron Crowe and Roman Coppola.)
But the best ad made by the Coen brothers—and, I would argue, a legitimate rival with "World Cinema" for their best short film—was made for a Swiss cigarette brand called Parisienne, which also commissioned ads from David Lynch, Robert Altman, Roman Polanski, and Jean-Luc Godard (among others). The Coens' contribution features a somewhat heavyset actor in a pinstriped suit eagerly performing "Wait 'Till the Sun Shines, Nellie" for a world-weary theater director. Something about the performance moves the director, who demands that the man sing it again. With its combination of Americana, caricature, and the comedy of the unexpected, the spot is unmistakably the work of the Coen brothers.