I've quit all games at lower levels than noble, and I was winning clearly in all of them before quitting, which I did with clear advantages, because I just thought it was too cheesy + I was reading all of these strategy guides which talked about 2 starting techs, and at lower levels than noble you start with more than 2 techs, so I felt really bad about that.
But I've quit almost all other games, too. I've quit a lot of games because I REXed heavily and neglected my army, I've quit because I failed the early rushes (mainly as a result of having little patience, in many of those failed rushes, I managed to get the rival's capital, then failed obviously lost battles, just cause I wanted to gamble). I also quit a game for losing liberalism, I quit games for being disappointed with what I was teching in 500 CE for instance (researching CS so late seems very disappointing to me), I quit games because of failed diplomacy, although I could have handled it.
I've also quit games for personal reasons: I've quit games in which I had to rush Willem van Oranje or Pericles, who are my favourite leaders, simply because I didn't want to kill my favourite leaders.
And... of course... I've quit games in which I was going for random leaders and drew the likes of stalin or mao. I've been able to sell myself the story that "it's just a game" with things I seriously hate, such as slavery, because not using that civic means little chance of success early on, but I haven't yet been able to sell myself that story for playing leaders whom I despise in real life. And... of course, going for random leaders, I've also quit, on the first turn, games in which I drew leaders I had recently played as.
I think I've finished about 5% of the games I've played. (I'm not counting the random leader games which I quit during first turn, just to get a different leader... those would seriously drop my percentage)