These days, it probably averages a game a year. But I have a penchant for playing games with large maps. Sometimes I'll pick up a GOTM game, and play it in 10-20 hours... which is quick compared to most contestants, but I'm not trying to finish on the leaderboards. Otherwise, I tend to be play long, epic games, in recent years either the Rise and Fall of the Roman Empire mod, or a game for a story I'm writing, in which case the writing part of it takes at least close to as long as the game itself. IIRC, for the longest story I wrote back in 2007-2008, the game's count of the playtime was around 270 hours, which would have included some writing time but little of the editing time. That's my longest-playtime finished game to date. Probably 10-20 hours of that was AI turn times as well, as they peaked at around 5 minutes on the old Pentium 4.
These days, I find that in any game (Civ3 or otherwise), I tend to play the game quite a bit for 1-4 weeks, and then become a bit tired of it, and move on to something else. I might come back in a year or so, but typically start a new game at that time. So a lot of games don't wind up getting finished. I think this is in part because I have access to far more games now than I did in my Civ3 heydey, which was roughly 2003-2009. Having a 9-5, my own place to live, and transportation so I can go out and do things more easily likely also contributes to why I don't finish a lot of games.
I actually like Civ4, these days about equally with Civ3. My computer couldn't handle it very well back in 2005, which led to my migration back to Civ3 in 2007, but when I revisited it in 2009 with a computer that could handle it well, I found it's actually not bad at all. It's generally like Civ3, but with more depth, and is the most moddable version of Civ (albeit with a steeper learning curve than modding Civ3). I'm sure I could dig up some posts from the late 2000s where I wrote about why I preferred Civ3, but these days I have trouble remembering what those were - the different artillery model being one, but that's less irksome in Beyond the Sword (Civ4's second expansion) than vanilla. I think the larger empires of Civ3 were another point against Civ4, but with faster computers these days and the ability to play larger maps, that is less noticeable now. In my current Civ4 game, I have 47 cities - enough to feel like I'm ruling a real empire, even if I would have had more on a Civ3 Huge map.
In short, Civ4 is spiritually an evolution of Civ3, and gets a lot of the "like Civ3, but more so" aspect right, at least if you play it with expansions. If I'd waited until the expansions came out before buying it, I don't know if I would have come back to Civ3. But as it is, I enjoy both iterations, and go back and forth between them nowadays.
Civ5, by contrast, changes a lot of things, notably the military (1 UPT) and expansion (heavy penalties for over-expansion, much harsher than Civ4, which in turn is harsher than Civ3). I gave it one more try this winter, but have concluded that even with the expansions, I just don't enjoy it. I haven't tried Civ6 yet, largely because it appears to be a spiritual evolution of Civ5, much like Civ4 was a spiritual evolution of Civ3.
