The old games loaded from cassette taught me how to be very, VERY patient, and text adventures taught me how to say the same thing in several different ways. They also helped me increase my vocabulary, including swear words.
Adventure/rpgs with puzzles involving objects taught me to think laterally and to try every conceivable combination before consulting the hint book.
Mount & Blade and Oblivion taught me that I love HORSES! *Clippety clop clippety clop*
Space games in the vein of Elite and the X-series taught me that I am not business-minded yet I can handle a ship pretty well.
A lot of FPS games taught me that stealth and sniping can remove the problem before it gets anywhere near you.
The Thief games taught me the same as the FPS and that light is my enemy but I can't see in the dark. It taught my husband to turn the brightness up on the monitor to cheat.
The Fallout series taught me that ghouls can be your friends too.
Online games taught me that I can't do everything by myself, yet it won't stop me trying! Oh, and not to rely on other people necessarily. :/
A lot of games (particularly adventure/rpg games and historical games) taught me some history as well (Gabriel Knight has been particularly interesting recently). They also taught me about different weapons, armour, etc.
Oh, and finally, most rpgs where you have an inventory with limited space and/or encumbrance taught me that I am a hoarder! A case of 'that might come in handy later' syndrome!