Tim Cavanaugh already mentioned one of my nominees for the next libertarian film festival: Death of a Bureaucrat (1966), a dissident Cuban comedy that feels like Kafka crossed with Laurel and Hardy. Here's a few more suggestions:
The Evil of Frankenstein (1964): Fans of Hammer horror usually neglect this movie, largely because director Freddie Francis isn't as capable as Terence Fisher, who helmed Hammer's other Frankenstein films. But I adore the story, which treats Peter Cushing's Dr. Frankenstein—a contemptible figure in the subsequent series—as an individualist hero driven by his love of scientific innovation. He runs into three characters who represent three different sorts of villainy: government repression, religious superstition, and corporate fickleness. (An entrepreneur of sorts is initially helpful but proves susceptible to—how shall I put this?—non-market pressures.) If I liked Rand I'd call the movie Randian.
Theodora Goes Wild (1936): One of my favorite screwball comedies, this picture mocks small-town prudes and censors—then turns around and mocks the thinly masked parochialism of those self-styled urban sophisticates who look down on small-town prudes and censors.
Death Wish (1974): I made the case that this was libertarian here.
Fast, Cheap, and Out of Control (1997): Errol Morris' best documentary. It's all about spontaneous orders.
The Gleaners & I (2000): Another documentary. I suppose it's more left-anarchist than anything else, but rightward-leaning libertarians ought to appreciate it too. I wrote a bit about it here.
The Oklahoma Kid (1939): I'm still trying to figure out how this one got past the Hayes Office. It's the sort of western most people believe was invented in the '60s or '70s. Jimmy Cagney's character denounces laws, governments, empire, and the treatment of the American Indian … and he's the hero. Not a great movie by any means (aside from White Heat I'm not a big Cagney fan), but it's a fun curio.
The Outlaw Josey Wales (1976): Another anarchist western. Clint Eastwood's best picture.
The Wizard of Oz (1939): Someday I'll write a long essay on all the libertarian themes in this film. For now I'll just note the pleasure of watching a movie that can distinguish giving someone a diploma from giving someone a brain.