Fear and Loathing in Las Vegas

It took a good many tries to get Hunter S. Thompson's 1971 novel Fear and Loathing in Las Vegas to the screen; Ralph Bakshi even once tried to get an animated version off the ground. Even the attempt that finally made it out in 1998 hit a few potholes on the way. Bruce Robinson was originally approached to direct, but refused. Then Alex Cox was hired, but stars Johnny Depp and Benecio del Toro weren't happy with his vision. Finally, Terry Gilliam came on board, and, quite honestly, I can't imagine the film working without Gilliam's particular style. 

Brazil

John Scalzi described Brazil as "dystopian satire" and that's a fitting description for Terry Gilliam's 1985 1984-esque film, though I think it could be argued that all dystopian fiction is a form of satire, since it is usually a vision of some aspect of current society ballooned to absurd and dangerous proportions. Brazil is the second film in Gilliam's "Trilogy of Imagination" -- along with Time Bandits and The Adventures of Baron Munchhausen -- focusing this time on the escapism of a middle aged Jonathan Pryce living in a dystopia (reminiscent of the vision of hell in Black Orpheus) of incompetent bureaucracy -- so incompetent in fact that acts of "terrorism" are just as likely mislabeled failures of infrastructure and "terrorists" suspects can be the result of printing errors.

It's brilliant and beautiful, if rather fatalistic. It was that fatalism that led to Gilliam's infamous duel with Universal. The studio itself released the so-called "Love Conquers All" cut with a much happier ending and nearly an hour less footage. Gilliam for his part debuted the film without Universal's approval in a college film-making "seminar" in Los Angeles that was open to film critics. Before it was even properly released to the public it had won Best Screenplay (and Gilliam Best Director) at the LA Film Critics Association Awards.

Time Bandits

Terry Gilliam's 1981 fantasy film Time Bandits is a polarizing film, it seems. If you experience it at a time when you can relate to the main character, a put-upon boy with a Roald Dahl-ian family life, it may be your favorite movie of all time. Elsewise, well, you may not like it at all. It's a movie that is successfully written (and often physically shot) from the point of view of its young protagonist, running on child-logic and attacking some pretty big questions as best a child can -- Kevin asks the Supreme Being why evil exists and is told "I think it has something to do with free will." Of course it's also a Terry Gilliam film, so maybe that's why some people just don't like it.