Yes. 80% of them at least, which means you can play all of the good games (your Halos, Ninja Gaidens, and Project Gotham Racings). The other 20% you probably won't care about. Check the Microsoft site for detailed info on which ones exactly will/won't work, just in case you have one that won't work.
can you play regular xbox games on the xbox 360?
Linear Mode
