I started my dabbling with Civilization III's scenarios with a fond memory of the Sengoku scenario. I recall liking the Daimyo units, which were an extra powerful infantry unit that you could upgrade as your technology improved. While my memory of the Daimyo's power was overblown (yes, they're strong, but if your's dies, it's a game over, so that limits their practicality), the scenario itself was pretty charming. The simplified tech tree and highly detailed map of Japan gave it a very different feel than vanilla civ, and the shortened time period lent it a nice specificity. In the end, I quit because I found myself at the end of the tech tree with something like 300 turns left to go, and even though I was the most powerful faction on the map, I couldn't actually win unless I started an interminable war of conquest that simply did not appeal to me at all. Plus, my well-developed cities were starting to develop pollution, and I was like - nope.
That's what I'm going to remember most about Civilization III - the damned pollution. It is unfair, I know, to judge an entire game by its worst mechanic, but it's just so persistently annoying that I can't help it. It never ends. There's never a point where you finally have your civilization under control. You have to remain eternally vigilant. That's true to life, I suppose, but I don't actually play 4X games because I want a simulation. I simply enjoy the sensation of painting the map with a semblance of order. Disorder bugs me. Especially in this context, it gets under my skin in a way few things can.
Still, that's only about 10% of the game. The other 90%, the pollution-free portion, was more or less classic civ. Once I figured out the necessity of aggressive expansion and the obsessive pursuit of resources, it played a lot like a more primitive version of the games that I'm used to. There's nothing wrong with that - it would be downright perverse of me to expect an early game to be more sophisticated than the games it inspired - but I can't deny that it suffers in comparison.
I think the thing I am most looking forward to about playing Civilization IV and Civilization V is being able to see the development of the series in a relatively short frame of time. Pollution aside, I can't help but think of Civilization III as a fairly "classic" take on the Civilization formula. When I think of the series in the most abstract terms possible, the game I'm thinking of looks a lot like Civ3 (I'd completely forgotten that Civ2 did not have a diplomatic victory, which makes it just a bit less iconic in my eyes), so while it may not have the enduring legacy of being one of my go-to games (which, let's face it, is not an honor that's going to be gracing people's mantlepieces any time soon), it is nonetheless a solid game, and well worth playing on its own merits (pollution notwithstanding).