Halo CE is probably my favorite game of the past 20 years. I enjoyed playing it on LAN with my friends back in the day. Halo 2 was great as well, and it was not only the first game I went to a midnight launch for (I actually got sick because it was cold out that night and, in my haste to leave and get to GameStop, I left my jacket at work), but it was also my first experience with online gaming (also, the Xbox had broadband support out of the box, something no other system that gen did). It had some other games I enjoyed as well, including Dead or Alive 3, Burnout 3, and several notable cross-gen games. The Xbox also had two analog sticks, which were offset, and offset sticks made the controller feel great in my hands (I didn't mind the "Duke" controller, though the "S" controller was better overall). I spent more time on the Xbox than any other system that generation (the GameCube was second).
The Dreamcast did have a few gems of its own, including the greatest fighting game ever made (Soul Calibur), but Xbox wins out for me.