In 1977, filmmaker Charles Burnett submitted Killer of Sheep as his Master's thesis at UCLA Film School. It's set in the Los Angeles neighborhood of Watts and filmed in an Italian neorealist style. After a well-received festival run, it languished for 30 years without a theatrical release or distribution because of music rights issues. It wasn't until 2007 that the rights were secured, and the film went on to have a theatrical release. Burnett isn't the only filmmaker who has run afoul of music rights. Abel Ferrara's 1992 film Bad Lieutenant used the song "Signifying Rapper" by Schoolly D, including in a key scene where a nun is sexually assaulted. Schoolly D's record company had not cleared the sample of Led Zeppelin's Kashmir used on "Signifying Rapper." Zep's people sued, and the upshot was that Ferrara had to destroy all unsold copies of the film and change out the track.
This climate has had a chilling effect on independent filmmakers hoping for a theatrical release. Many major label tracks are made available with a "festival license" option, meaning you can pay to use it on a version submitted to festivals, but if you plan distribution beyond that, you have to pony up big bucks. Luckily, this has led to many more independent filmmakers seeking out tracks from unsigned musicians for much more reasonable terms. At any rate, you should check out Killer of Sheep if you haven't. The songs really do make several of the scenes work, and you'll appreciate that Burnett stuck to his artistic vision, even if it took 30 years for most of us to be able to see and hear it.
Killer of Sheep: The Charles Burnett Collection (via Amazon)