At IndieCade 2011 this year, I led a discussion on the idea of depth in games with my friend Paul Sottosanti, who is not only a great designer, but he is also one of the two elite SpyParty playtesters. We decided we don't really know what depth in games actually is, so instead of trying to give a lecture about it and flail around, we simply asked the audience what they thought.
Paul and I gave quick intro talks about our thoughts on the topic to get things started, and then we opened it up to questions and comments. I put a slide up at the end of my short talk to try to tease apart some of the things people often conflate with depth, and it had this taxonomy of ideas:
I gave a short list of games I think are work thinking about when pondering these ideas: Go, Poker, Counter-Strike, The Sims, Super Meat Boy, Shiren The Wanderer, Dwarf Fortress, Braid, Thief, Little Big Planet, and Spore.
I also think this is all loosely tied to ideas from philosophy about the difference between the Beautiful and the Sublime, some discussion of which you can find here.