Best game since 2001?
It's not my favourite game, nor was it the one that I had the most fun with, but Red Dead Redemption was and, honestly, still is the most impressive game that I've ever played. A tight and interesting story, believable characters, and a spectacular ending. The thing that really wins it for me, however, is simply how real it felt. Unlike, say, Oblivion, the wildlife was totally and utterly seamless. The landscapes were utterly stunning, and walking down the main street of Armadillo was utterly incredible. The NPC animations were all perfectly fluid, and the town felt alive. Although I have high hopes that Skyrim might match Red Dead's achievements, that is, for the moment, just speculation.
TL;DR: Red Dead Redemption. Not my favourite game, but far and away the most impressive game that I've ever played.