Civilization Revolution, assuming you have a PS3 or XB360.
It's the core Civ experience distilled to the point that pretty much anyone can play it. Also, on the lowest difficulty level, the tutorials are quick, unobtrusive, and walk you through the gameplay; also, on that level, it's almost impossible to lose the game, which strokes your ego and says, "See? Strategy games aren't so scary."
Once you master the ropes, the highest difficulties really pose challenge where you REALLY have to know the strategy mechanics and be able to exploit choke-points on the map to come out on top.
Old-school Civ fans tend to hate on CivRev because it's very streamlined and very easy compared to the original series, and, yes, they're right, but that, to me, doesn't inherently make for a bad game; it just makes for a bad game if you're expecting all the details and nuances of a core Civ game.
CivRev is a strategy game that you can play, start-to-finish, in just a few hours. It doesn't include a lot of the more micromanaging details that can make a strategy game daunting to newbie, and it also happens to be one of my favorite games of all time.
EDIT: 1000th post?! Damn! I was going to start one of those "It's my 1000th post so I made a special thread" threads... Oh well...