Ah yes, Civilization. From the very first one on an MS-DOS machine to the Gods & Kings on a powerhouse, Civilization was and will remain one of my favourite series.
Civilization 2: Gold Edition allowed multiplayer. I've got a lot of amazing stories from this one, but will keep it at one (for now). Me and a close friend were playing an open game (meaning anyone could join), and we're a day into the game when a stranger enters and joins the game. He then proceeds to kick both my and my friend's ass until we're left with only our starting capitals. He then left the game, never to return.
The stunned silence from me and my friend seemed to last forever. What the F just happened?
Civilization 3 - You can conquer cities by having enough cultural influence. France, with its mighty armies, would destroy my units and conquer my cities, but a couple of turns later, my Egyptian culture was high enough to win the cities right back. What followed was a game of back and forth, until my cultural output got so ridiculously high that I was starting to conquer original French cities. Taking Paris had never been so easy.
Civilization 5: Gods & Kings - This game introduced Faith, allowing you to found Religions. Playing with a friend, I found out that you can actually change the name of the Religion you are founding. I won't go into detail, but I laughed my ass off, and finding the silliest names is now a tradition in our games.