After reading a lot more of this thread I decided to post a few more that I don't think have been mentioned.
Sydney - Paul Thomas Andersons first feature film. Starring John C Reilly and Phillip Baker Hall (Samual L Jackson/Paltrow also in it). Really great and I got the PTA feel after the first few shots, he really has a unique visual style imo. Also known as Hard Eight.
Pump Up The Volume - Christian Slater as a rebellious teenage radio host.
Swear To Tell The Truth - Academy award winning documentary narrated by Robert Deniro about legendary comedian/freedom of speech martyr Lenny Bruce. However this is going to be very hard to find legitimately considering you can't purchase it because the music rights were just way to expensive (a lot of classic jazz tracks). I believe it's being showed weekly in some museum in NYC but I forget which exactly. Must see in my opinion and a shame it's not easily accessible.
Big Trouble in Little China - Probably the least obscure film I've mentioned, but it's just such a great action/comedy and there are so few similar movies that are on it's level. It accomplishes exactly what it sets out to and the Russell+Carpenter combo always delivers.