I had to put down my dog in August. Her name was Amelie. Visually, the most beautiful movie ever made. That director is an artist. Great movie, too. It's like the French Wes Anderson. This would be my vote in this year. By a C-hair.
Close second for me is Vanilla Sky. IIRC, this movie didn't blow up many skirts, but I fucking loved it. Soundtrack is amazing. This movie alerted me to the existence of Sigur Ros.
Monsters Inc, IMO, is possibly the best Pixar movie. I'm not the kind of adult that loves Disney movies like some. I usually suffer through them. I have zero problems when my kids want to watch Monsters Inc.
I'm surprised Zoolander isn't in the pole. This is highest-level comedy movie execution. Who doesn't quote something from this movie at least once per week? I have a hard time choosing a comedy movie for "best picture" on just about any year, but this at least deserves best-of billing.
Black Hawk Down is incredible. One of the few war movies I've watched multiple times.
As cheesy and bad as it is, it's hard to argue that Fast and Furious wasn't a cultural phenomenon. Not a great movie (although fun to watch), but boy did it have an impact on popular culture.
What a strange year. Again, there's no Shawshank or Good Will Hunting or whatnot here that you have to vote for, just a bunch of really, really well executed movies spread across very different genres. It's hard to compare one movie to another, as they're all trying to do very different things.