are xbox games compatible with an xbox 360 and vise versa?

You can play some xbox games on the 360, but not the other way around. You may, however, need an update from xbox live for them to work. I tried to play an xbox game on my 360 and I got a message that said that it needed an update. But since I can't connect my 360 to xbox live (my internet connection is wireless) I couldn't play the game.

I think you can play certain xbox games on the 360 but not the other way round.