From the movies which I have seen, only three films would be what I consider great and one of them isn't even released in the US until 2004 (Hero). The other two would be Return of the King and Mystic River. There were a number of good films, but doesn't quite do it for me: Lost in Translation, X2, Big Fish, Master and Commander. And of course a whole boatload of mediocre movies.
On the other hand, there must have been a record number of truly horrific films. By this, I don't mean just bad, but ones that you wouldn't see again if you got paid to do it. Of the movies I've seen, these all got F ratings: Phone Booth, Holes, Legally Blonde 2, Matrix Reloaded and Revolutions, Daredevil, and 2 Fast 2 Furious. Several others were pretty close. Some others which I have not seen but heard awful stories about: Gigli, Cat in the Hat, Bad Boys 2, and Mambo Italiano.
I am talking actual movies here; there were quite a few outstanding acting performances including one which I consider the best given by anyone so far in the 2000's, that being Charlize Theron in Monster. It's the best performance I've seen since Ian McKellen in Gods and Monsters.