non-sense (Score 1)

A lot of good "fun" examples have already been mentioned. Twister, Jenga, You Don't Know Jack, the multitude of party games so entertaining and asinine that all the joy is in the playing, not the winning. Strategy games with luck and/or cooperation/coercion: Monopoly, Illuminati, SoC. Any game that distracts from the actual playing of the game.

When you get into pure strategy games like checkers and chess and Go and Abalone and Othello and countless others, there's a much higher immersion factor. Everything is concentration and intensity. Much like any competitive sport, your success hinges entirely on *your* performance. There is true measure between you and your opponent, and that is where your instinctive competitiveness kicks in, and it makes the game that much more intense, particularly in games where every piece you lose makes it harder for you to win.

However, this is also a test of sportsmanship. The ability to realize that you are playing a game just like any other. And that is something that should be taught early on. Sometimes you have to lose a whole lot before you can win.

As far as the connection between games and "mentality," I believe the games we play are a reflection of *us*, and not the other way around.