Catan (board game) taught me the power of being forward-looking but also being myopic depending on the type of your opponents. It also taught me that I don't belong to games (situations) where one party is being irrational and acts based on knee-jerk decisions. In Catan, I now try not to reveal my best card and get ahead early on in the game in order to avoid becoming an easy and default target for other players. I think these are really interesting life lessons I (re-)learnt from a game that wasn't even designed with that purpose in mind.
I'm looking for any and all games that can potentially teach me something, but are not "educational" games.