I've never played any Civ games, but is it one of those games like the Sims or The Movies where you can build stuff and then the game gives you lots of chores to do?
No, not really. I'm with you on the Sims. Played it for a while -- I can somewhat understand the appeal, but it wore off pretty quick. Deciding when to poop and when to wash the dishes is something I get to do in real life, so the simulation aspect seems a little wasted.
But the Civ games are very different. There's a huge element of strategy (and on a grand scale). Also tactics and resource management. In a nutshell, you are the dictator of an ancient culture at the dawn of civilization (I play the Chinese and the Persians a lot...) You're given a map of your surroundings, which you gradually uncover as you explore. There are various resources (food, minerals, money) on the map along with bonus resources and "special" resources (iron, gunpowder). You build cities in order to best exploit these resources.
You have to decide how to best manage your nation to compete (and eventually dominate) the other nations out there developing at the same time you are. You can use different strategies (Rapid population growth, militarism, financial domination, scientific research, etc) by choosing what each of your cities devotes its resources to building.
It's really a hell of a game. The variations I've enjoyed most have been Civ II and Alpha Centauri. Stay away from Civ Call to Power.