from my experience (2-3 ps3 games and 15 or more 360 games) they come with the original case and in perfect condition, but the game itself is another matter. (scratched but playable)
I dont know if this would work but what I do is put the sticker under a blow-dryer for a couple seconds and usually it peels right off, and if it leaves any residue just use some adhesive remover (if you have any)