It's hard for me to remember a game in which I actually learned something. I believe this is in part because when we are playing a game and having lots of fun we don't really think of it as a learning experience. A game that teaches us something is more like pure enjoyment and of course entertainment. Of course, there are many exceptions to this: Mainly if we are playing a game that we actually know that is intended to teach us or help us learn something.
As a musician, I can remember playing a game that a friend and I invented (and probably the only ones that played it). The purpose was to play the 'most difficult --or crazy-- combination of two rhythms' with our hands. Basically, we had to come with patterns and perform them right. For example, we tapped 3 beats with our left hand, while tapping 4 beats at the same time with our right hand. This specific example would be a '3 against 4.' We did it with 4 against 5, 2 against 5, etc. We where actually creating music and working with a quite advanced concept of rhythm called 'polyrhythm'. It was lots of fun, but I am sure that not many kids will play it.
The interesting thing about this game is that I still remember (and use as a professional musician) many of the rhythms that I learned during those games. It is quite impressive to think about it. I learned complicated rhythms not in class, or with a teacher, but during school break and with a friend: just challenging each other. I remember using pen and paper to figure out exactly where to place each beat, in other words, we worked hard on it! The only gratification that we got from this game was the satisfaction of being able to perform a complicated rhythm.
