I've got a normal Xbox, not a 360. Also a Playstation 2. Haven't bought any of the newer consoles. My favourite games on the Xbox are Shenmue II and Jade Empire. Shenmue II was great, a 3rd person martial arts adventure game in Hong Kong, set in 1987 - and when you walk into game arcades in one area of Hong Kong, you can click on the arcade machines there, and it lets you play SEGA's old 80's arcade games :)
Mostly I find, though, that I prefer playing PC games.