This post was going to be entitled "games that make you think", but that would not be a precise description, and would end up leading to a debate on serious games. Plus, it could generate arguments such as "all games make you think". Those are valid discussions, and we might address them in the future but, for now, that's not what I mean.
A good comment on lateral thinking through games was once made by Gonzalo Frasca in his post about Warioware and the DS:
It was a nice experience, I could enjoy the match while having part of my mind thinking about other issues. Pong is the radio of videogames: you can play while doing other things.
I guess different games stimulate different forms of lateral thinking. For instance, I remember Worms Armageddon's Ninja rope training (the one where you had to keep swinging and collecting objects) as being great to formulate arguments and counter-arguments for hypothetical discussions. While I can't recall any actual topics, I remember vividly how I thought that game was a great exercise in dialetic (!).
Of course, this feeling could be limited to casual, close-to-casual, and mini-games, although racing games also have a similar effect on me. Plus, games with highly repetitive tasks might lead (or so I've read somewhere a long time ago) to a state of mind similar to meditation - which I'm not sure could be classified as lateral thinking, since it seems that it actually is the absence of thoughts (and in that case, it also might get its own post in the future).
Anyway, since we've been talking about unusual sensations caused by games, I thought of sharing this...