I know I really enjoyed NFL 2K (2K was a Sega company before being spun off), but can't remember the specifics of the game. I mostly enjoyed a lot of the fighting games -- Power Stone, Dead or Alive, Soul Calibur - as well as Crazy Taxi.

Dreamcast was awesome. I seem to recall it had a football game where you could take control of an individual player who wasn't the QB or ball carrier for the first time. 

grayruby

Currently, probably the Xbox, but the Dreamcast is probably my favorite one that I've ever owned.