As was said, the popular Xbox games have been ported to the 350, and indeed many of the most successful are now directly downloadable to the console from the Xbox Live Marketplace, marketed under the title "Xbox Originals".But XBOX 360 is backward compatible to old XBOX games, correct?
If you get a 360 now, I highly recommend a Gamefly account. There's a lot of catching up to do. October by itself will nearly bury us under AAA games.