The concept of growing and managing a civilization from ancient times and forward is like a honeypot to me. There is much diversity to do this as you can play maps that are modeled after planet earth, or you can play random maps (my favorite are the fractal maps), there are plenty civilizations to choose with hundreds more thanks to mods (I've been interested in a pokemon civ game lately, after I found various pokemon themed civilizations. I would like to do a game playing as Wigglytuff's guild against the other regions, sinnoh, johto, kanto, etc. Any other poke'fans out there?), unique abilities and unique units give you the option to totally act (role-play) how that civilization you play theoretically would have behaved, you can just roll everything randomly (my favorite thing to do) and just roll with the punches of what was randomly rolled and what happens as the game goes.
It is pretty fun to compare the games you play to actual history. I am playing as Maya in my current game and I built machu pichu (not mayan... right?) in the city chichen itza, Ahmad build the chichen itza wonder in one of his cities, Poland got steamrolled by Songhai (this is the first time I have ever seen songhai actually do the domination, I usually see songhai get conquered) The development of Greece was set back thousands of years since they settled so close to my borders and compelled me to initiate a war (greece vs maya?). Things like this are very fun. =D