Depends on what you mean by "deep." If you mean well-written with characters that at least act and seem human, then yeah, Prince of Persia, Silent Hill, KOTOR, Eternal Dakrness, pretty much everything that's been mentioned. I'd like to add Link's Awakening (the old game boy one) to that list just because of the ending is a massive contradiction to the entire game.
As far as games making a statement that reveals some inner-truth about human nature or enlightens some fact about society, Grand Theft friggin Auto. It really states alot about us as a people how much we *would* enjoy the life of a car jacking, prostiture hiring mass murderer if there were no real consequences to it.