I personnally end less than 1% of my civ games.
First, some games are just too desperate. When you start on a small chunk of land surrounded by mountains, there is nothing wrong in restarting immediatly.
Conversely, I also quit when victory is very likely. Since I play smarter than the AI (better management, better tactics), then, when I can see I am ahead on the histograph, in research and in all relevant demographics (mainly pop and area) and I have access to all strategic resources, I see no point in finishing out the AI civs.
In fact, I quit whenever the challenge is too low or next to impossible.
Furthermore, I like early and mid ages better: exploring, colonizing, struggling for land... that's where the thrill is. I hate the lategame where you mainly stare at your computer screen waiting for the AI to finish its Brownian unit moves.