I've recently started playing this game and am adapting to it much more easily than I did to Civ III. I started out on Civ II and it has been one of my favorite games since, but I could never really get the hang of Civ III. So far, my normal strategy of founding as many cities as I can and placing them so they cut off the areas where my rivals can expand into is working great. I've played one game on Chieftain just to get a feel for the game and see what's different, and now I'm working my way up the difficulty levels.
I just finished a game on Warlord difficulty with a space race victory. I almost got through the entire game without going to war (either declaring war or having war declared on me), but when I was halfway finished building my space ship, France (who was one of my friendliest allies) just randomly decided to declare war on me. I managed to stomp him into the ground in a few turns, but I was seriously annoyed that I had to spend so much gold and divert so much production in order to wage war so late in the game and he managed to destroy several improvements before I retaliated.
Now I'm going to play one on Prince, but this time I won't be so nice.