For the Xbox 360, an initial list of compatible Xbox (1) games has been posted. This is a good start, but I notice that Burnout, Far Cry, and Otogi aren't listed. I've been playing those recently... Ah well. I do have my original Xbox, so it isn't like my life is ruined.
The main point here is: keep both systems. In about a year, the library for the 360 will be large enough that you will have more than enough games to occupy yourself full-time. At that point, you can toss your Xbox and its games.