Man, some of you guys got saddled with sucky girlfriends. My wife is always down for learning a new game and can usually pick it up on the first read through. At times I might have to do the point calculations or run the upkeep portion for her but as far as tactics goes, she can figure it out quickly.
But since she has never read the instructions to any game, she can't TEACH a game to save her life! Something about reading instructions gives you the sense of order and flow, if you just learn every game from experience you miss out on that.
I played Quarriors for the first time a few days back. I like it so far, though like many card driven games there are lots of questions about the order of events or how things should work. I think I have a decent grasp on it, will introduce it to my casual gaming group next week. Also go the Red Dragon Inn game, for the same casual group. I still think King of Tokyo is one of the best casual games out there, fast enough to just teach as you play, simple enough for even the densest clod to understand, and thematic enough for the lightbulb to flicker on in even the most unimaginative player. I play too aggressive though, I'm almost always knocked out early.
If you don't have much of a game group, check out the solitaire games. Most of the co-ops can be played alone, as can most open info wargames (and even lots of simpler ones like C&C) and there are plenty of solitaire only games, check out VPG and DVG. Of course in the internet age there isn't much reason for playing alone, but I have a hard time wanting to play boardgames electronically, not sure why.