I finished a game of Civilization III that had been started about five or six weeks ago but had to put aside. The delay meant that I'd forgotten some of my plans (I didn't remember to change to a democracy until the 1860s). Most of the earier games I'd played using a cultural strategy where I would absorb other cities or be first with the technology. This time I decided to try a military strategy and chose to play as Germans (that culture has a military emphasis). However it turned out that my neighboring Romans were culturally weak so I was absorbing their cities and didn't focus on anything military until fairly late in the game. This was also the first time I'd played on a huge map ("huge" is one of the size choices) which I'd hoped would give me time to establish my civilization before conflicting with others. Unfortunately the size meant that each civ was so large that it pretty much had most of the needed resources and luxuries, limiting the opportunities for trading (or need to go to war to gain control). Next time on that size map I'll increase the number of civilizations so that it'll be a bit more interesting.
A problem with Civ3 that I don't remember with Civ2 is that there are now some serious slow spots in the game, usually in the middle after all the initial exploration and basic research has been done but before the endgame space race. The tech tree seems to have been simplified a bit so that now after the first quarter of the game every culture is pretty much researching the same thing. It would have been much more interesting if even into the early 20th century there was a strong possibility of pursuing different research paths so that say one culture might go after strong military technology but another more advanced commercial institutions (there are potential play balance problems but shouldn't be anything crippling). There are also too many spots where cities have been developed as far as possible leaving you again with no real choices and each city being different only in the effects of its placement (admittedly a potentially strong difference: one city might be a poduction powerhouse and another otherwise identical city a weak one due to the terrain).
I'm surprised that nobody has yet--as far as I know--explored the politics embedded in the Civilization games. There's plenty here: about how different cultures are considered to work (such as the military advantages for Germans), winning conditions, control of the environment, how the game rewards physically large civilizations or those with lots of cities, the effects of religion, etc. These aren't necessarily negatives even if some of them seem dubious.