Do Xbox games work on a Xbox 360?

Yes, about 300+ X-Box games work for the 360. However, you can only play them on the Elite, or you can get a software emulator for the original 360/360 Arcade.

Go here for the list of compatible X-Box games:

http://www.xbox.com/en-US/games/backwardcompatibilitygameslist.htm

UPDATE:You cannot play Xbox LIVE on Original Xbox games. :(

Hope This Helps!

-MidKnight777, DevinUser514