I finish about 75% of the games I start playing as "games" - that is, games where from the start I intend to be "the ruler" of whatever civ.
I rarely finish "experimental" games - those are games where I'm just testing out ideas and playing 200 turns. I play a lot of these games because I love the opening when everything seems possible and because I like trying out different ideas. It really helps to learn a civ's strengths quickly and makes me aware of how dramatically the map effects play. Everyone knows that, of course, but we forget and make strategy/tactics suggestions as if the map was a minor thing.
Things that make me play a game to the end: losing (I like to make the AI earn victory), amusing map (once I was rolling up X shaped island like tic-tac-toe), finishing a certain victory condition (everyone FoL).
Things that make me not finish: winning (if I know I've a win, I don't need to have every enemy's head on a pole), going into the endgame in 3rd or 4th place (if they can't crush me or me them, what's the point), too big an empire (the huge map games can be dreary).