Christ do I love Civilization III. I've wasted so much of my life on it.
One thing that does bother me is that the AI is so obnoxious. They have absolutely no respect for your borders, but if you so much as build a free railroad for them they act as if you've pushed the world to the brink of total annihilation. They also have some strategies that make no sense from the perspective of someone trying to win the game and all the sense in the world if they're trying to make me just quit in frustration, such as fucking Babylon building thousands of bowmen in the modern era and slowly but relentlessly marching them towards my cities to do a "sneak attack". One can easily mow every one of them down, but it takes about half an hour of extreme tedium that I usually don't have the patience for.
Anyway, the feeling of taking the strongest enemy on the map and reducing him to a single city on an isolated desert island is one of the better feelings in existence.