Planescape Torment/Fallout is pretty deep in a computer game sense. Other than that most good games challange you in a way such it feels you've accomplished something, otherwise it would just be a waste of time.
A "hybrid" here is probably MMORPG:s such as World of Warcraft which are very rewarding, but because it involves so much time and work you will realize you have wasted time when you stopped playing. A great but short single player game will not haunt you as much afterwords, but it's certainly not as rewarding either.
There are of course a bunch of great "thinking" games, without being really "deep". Examples would be the text adventures (hitch hikers guide to the galaxy for example) and Monkey Island. No deep meanings there, but challenging.
Then we have a bunch of games which are very deep emotionally and socially, such as the older Final Fantasy-games. Final Fantasy 6 (aka Final Fantasy III) and 7 for example. They have deep meanings in a way.
Another kind of game is the "shower genre", which itself is so repetetive and monotone you can play them without thinking at all, which lets your mind wander freely like when you have a shower. These games are far from deep but they can help you think deeper.
Great thread btw.