I put A Clockwork Orange in there for a few reasons. It's far from my favorite film I should add - but as the focus is on 'groundbreaking' I'd say this broke ground in a few unique ways. Firstly the wider social commentary that the film inspired was unparalleled and still to this day evokes comment and reference in light of crime and youth. Secondly the censorship issue, it was rated X in America and was was of the first to be so. In the UK it was banned for 27 years and achieved a cult status because of it which only fed into the notoriety of the film which ultimately ensured a successful re-release. Thirdly, the use of the soundtrack - predominantly a Moog synthesizer. I think it was pretty unique for its time to soundtrack the film in a particularly stylised way that it did and it has been inspirational to cinema as a result.
Four Eyed Monsters was my wild card. Again, its far far from being one of my favorite films but this is truly a film set in the reality of 2007, the age of now - the web savvy twenty somthings and the 'myspace generation' for want of a better description. From its semi-fictitious storyline to its conception as a film and process in getting recognition when no major producer will back it is a story in itself but the way two people drove worldwide interest in the film - much of it online - is something I haven't seen before. It's an indie film down to the last and it's one of the few films where watching the DVD extras about making the film (which are also the podcasts and myspace videos) is more intriguing than the film itself and it's the real characters and the reality of two people trying to make a film successful against all the odds (money, representation, business advice, logistics etc) that makes this film groundbreaking in its method.
All just my opinon of course.