First of all if it says xbox 360....it should work.(remember it should say xbox 360 on the cover on the top or it wont work ok)
Secondly if you buy the games from game stores (eb games , Game)ask the store people if this can be played on your console and the requirments(just to make sure)
If you have very very old xbox 360 games and if you want play it on the newest version of the xbox 360 you might have a chance if it works..
But the most important just look at the requirements at the back of the cover of the game and see if it matches or if it could be played on it...