For the record, Mulholland Drive and Children of Men would have been my next two picks all being equal. Two incredibly well directed films that felt completely unique and which elicited really visceral emotional reactions when I saw them in the cinema. A few of my favourites have already gone, and I'd forgot they were even released around now. I think, having seen these picks, this isn't a draft I'll come near winning, just because so many of the choices will be influenced by seeing them in the cinema, and I saw a lot of great weird stuff while missing some big mainstream films.
It is a strange decade for cinema though, both underrated and overrated. Lots of great comedies and dramas and on the other side a lot of overhyped dross. 'Comedies' with quirk and not much else, like Juno or Garden State which are now (and were even at the time) excrutiating, terrible high-concept films that were 90% twist, mediocre graphic novel adaptations. Some of it has aged like fine wine and some like milk.