I'm afraid this topic might be "dead" already, but I will post anyway, since the things mentioned here made me think and I want to note what I thought.
First of all: Playing is one of the most important things for me. I actually take care that I play differnt things and that I play a little everyday. I believe that the ability to play, that is to train skills that are not really needed in every day live, is a sign of intelligence and among the animals I know only of dolphins that play.
http://www.youtube.com/watch?v=TMCf7SNUb-Q
Furthermore playing is simply fun. It gives me pleasure to understand rules, apply them as good as I can and see what can be created within certain rules. I find that often the most simple rules can create the most fascinating outcomes (e.g Go or Game of Life). Also I find that I learn faster when I play with things and sometimes I try to see theoretical stuff as a game, or better: as a set of rules that create a certain outcome when applied.
Games that tought me something:
-Spore --> I didn't like the game mechanics of the later levels too much, since they were basically RTS games, but the whole game gave me a better understanding of evolution. E.g. when some bodyparts that u needed in the water just dont make anymore sense on ground and hence u get rid of them.
-DotA --> This is actually the game I played by far the most. I played it in some different teams and with hundreds of different players from all over the world. And I thought a lot about, though a lot of these thought went were about possible tactics, by far not all were- It is through this game and through its community, that I learned about quickly forming a team to achive a goal, about group dynamics in short time intervals (a game takes roughly 1 hour) and also in long terms (A team exists for month and often breakes apart when the players develop at differnt paces, a important match was lost, or someone experiences great changes in his "real" life ), it told me about the possible consequences of blind greed, of being indecisve for too long and also of doing more than one thing at a time .
-The Marriage --> I'm not married and I don't think I ever will be, so I am in no position to judge, but through this game I at least got to know a personal view on the "rules of marriage"
-Home --> A strong impression of how it might feel to die in a home for the aged.
-WoW --> I didn't really play it, though it thaught me that many humans seem to like rising numbers, visual effects, cool names and so on. Without referring to WoW, it reminded me that many people tend to believe in the biggest crap if it only comes in a nice dress
I learned more specific things from different games, but I don't recall all of them right now. Also I learned something from the "act of playing" in general, however this is more a feeling or abstract thoughts, than something i could express at this moment.