I'm kind of looking into picking up a strategy game at some point, but I've always had problems with strategy games for a few reasons. One, I'm so used to playing RPGs, that the lack of substantial "story" and RP elements in most games tend to make me bored pretty quickly. Two, I'm not overly interested in logistics and mechanics and prefer to keep things pretty simple. If it gets too complicated and, yes, "realistic", I will simply find other ways to spend my limited relaxation time.

To give an idea of what I have enjoyed:

Lords of Magic
the Caesar 3 demo that came with Lords of Magic
Dragonshard
A lot of the "SIM" games (although the last phase of SPORE annoyed the heck out of me)

I also really enjoy the sort of "Stronghold building" aspects in games like NWN2 (original and Storms of Zehir)

In other words, what's a good Strategy Game for someone not into Strategy Games

Addendum: I do have a copy of Civ IV. when I initially installed it, I was annoyed that I couldn't do all the town-developing I could do in the beginning of Caesar 3 and wasn't inclined at the time to give it a shot anyways. I'd be more willing to do so now, but I'm still kind of sad I couldn't do as much town development