I, too, got my introduction to the Sims franchise by way of SimCity 2000. I was a huge fan of an old game called "Populous" (where you play the deity of a village and direct them to do the things they need to survive, fight wars with their neighbors and smite their enemies with godly powers) and I saw it as a modern version of that.
Unfortunately, it wasn't. SimCity wasn't a game I could play for extended periods of time. I'd play for a few hours, forget about it for a few weeks/months, then play some more. I just couldn't get into it. Then, I got a strategy guide for it for free from a friend of mine who worked at a bookstore. I figured maybe this will help me get interested in it (I really liked the concept, I just didn't like the game, because I had no idea how to do things).
On the back cover was an advertisement for Maxis' new game: The Sims. It wasn't even out yet. At first, I wasn't sure I was interested, but I kept seeing this ad for it (and a few others, too), so I figured I'd give it a shot. So when it came out, I bought it. I was instantly hooked.
I sort of lost interest in the first Sims shortly after Makin' Magic came out, but my interest was renewed the moment Sims 2 was announced. I started playing Sims 1 again until it was released. But I lost interest again, shortly before Apartment Life came out (I never got that expansion).
When Sims 3 was announced, I went ballistic once again. The day it was released, I went out and bought the collector's edition. I like this version more than I did the other two versions combined. In Sims 1 and 2, it was like you played inside a bubble. Nothing really went on outside the lot you were on. But in Sims 3, I love how the entire town is pretty much alive.
I don't see myself losing interest any time soon.