CIVILIZATION III / 2K Games / PC
Civ III basically plays it safe and delivers Civ II Enhanced. It has nicer graphics, a slicker menu system, and a number of gameplay tweaks and additions that complement the established Civ style rather than making any radical changes to it.
The one major shift here is a bit of nerfing of war and conquest as a viable overall victory strategy. There's a new "cultural influence" system that plays a bigger role in overall victory (in that it's much more viable to obtain in most settings), and there's a new factor of "war weariness" that influences your population if you're dragging around in wars for too long.
Civ III's other semi-major gameplay change is in the use of natural resources. Certain resources are now required to build certain types of units. I felt, if anything, this was the game's one big mis-step, because with the random scattering of resources you can wind up in too many unrealistic situations where you can't build a key unit because the one resource patch you need for it anywhere on the continent is under enemy control.
The minutiae of little gameplay tweaks for the truly hardcore is too much for me to get into; I enjoy small conquest-based games of Civ but I've never had the patience for games that last tens of hours and force you to micro-manage a whole sprawling world full of cities and units, so I can't comment on every little tweak and how it compares to the other games. I can unequivocally say it's a very good game on its own merits, and definitely better than Civ I. For players that are focused on aggressive military expansion, Civ II Gold might be the better choice as this game's changes seem specifically designed to jam that strategy up. Can't comment on Civ IV or V as I haven't played those yet as of this writing. But Civ III Complete goes for like 2 bucks on sale at Steam now and at that price it's easily worth checking out if you're at all interested.