Funny yours would be the reply before mine. I was just coming to recount that we had played a Civ 3 PBEM. I haven't played again since then I don't think. What I remember most was the visual upgrade from 2. Civ 3 was gorgeous for its time. I didn't like the crushing, "Distance From Palace," modifier. But, I wasn't as good a player then as I am now. Could have very well been user error.
As most folks know, I was a big 4 proponent. If I had half the time back I spent playing that, I'd be in my forties. I will say, after all those hours, I learned to hate, "The Stack Of Doom." I am not a very aggressive player, so, I was almost always unprepared for it. As much as I hated them, I also used the, "One unit per hex," rule of 5 and 6 to avoid playing either of them. Having generously been gifted a base copy of 6, I have to say, I am converted. The cartoony graphics are still off putting, but, they do a great job in keeping your eye on the prize with the UI that I am willing to put up with that quibble.