There have ALWAYS been "independent" films of course.  But with the gradual breakdown of the Hollywood Studio System in the 50s and early 60s, independent filmmaking really came into its own.  Shooting for just 14 days, and with only $400K to spend, Director Ralph Nelson ended up Producing THIS flick all on his own, when no major studio wanted to take on the project!

The result (Distributed by United Artists) garnered an Oscar Nomination for Best Picture (losing out to "Tom Jones").  It also got Oscar Nominations for Best Supporting Actress (Lilia Skala), Best Adapted Screenplay, and Best Black & White Cinematography.  But of course what everyone remembers is that this is the film that got Sidney Poitier his only acting Oscar.