I have been playing Civ since we got a PC bundled with Civilisation II: Test of Time (and I really want to see the multi-leveled maps of Test of Time come back some day - there was something deeply thrilling about being able to fly your ships up to the gas giant, or send your skeleton warriors down into the underworld). I own Civ III and Civ IV as well, and have played all three extensively.
But I'm not terribly good at it.
Realms Beyond is a forum/website stuffed full of people who are good at it. Their unifying theme was originally variant play - adding additional restrictions to Civ games, or altering the map to give a new experience. They've played vast numbers of tournaments in CIV (and earlier in Civ III); you can read excellent and extensive reports on a lot of them on the website of prominent member Sullla.
I am nowhere near the level of most people over there. But the nice thing about single-player games is that you can have fun even if you have no hope of winning. Sadly, Realms Beyond has mostly switched over to playing multiplayer games now, but I signed up just in time to see this posted:
Adventure Sixty-One: Pink Pride
Scenario: Realms Beyond has a long tradition of dotmapping, where you plan out your civilization by drawing colored dots on a map screenshot to place future cities. The most glorious of all dots shall ever be the Pink Dot. The Pink Dot signifies the most bold and daring settlements you can achieve, a long reach from your homeland into hostile wilderness, seeking great rewards of wealth and resources.
This map is crafted with a dismal starting location in the tundra, but many Pink Dot opportunities will await you as you explore. You are Catherine of Russia, whose Imperialistic and Creative traits should serve you well in your quest for Pink Dots.
Scoring: None. Just play and regale us with tales of your experience.
No scoring? Sounds perfect! Sign me up! So I renamed my capital...
... plotted my Pink Dotmap...
... and set off on an adventure filled with setbacks and disasters!
What? I said I wasn't very good at this game. ^_^