I've only abandoned one game in recent memory, it was a couple weeks ago and I set everything even my CIv to random, but I think I accidentally added more AI, started on an average island with Iroquis, Rome, Vikings and Persia (right next to me), I took out Persia, but it used up so much of my resources, that when Rome and the Vikings came by I was spent, I would have finished the game, but the Vikings were taking too long to finish me, even though I love watching Berserks swing those axes.
Usually if I've gotten bored and the game is going to Modern age I just build the UN and try to win diplomatically, even if I lose, it ends the game.
Since I like comparing my score from civ to civ, I try to finish all my games.
Interesting how ppl restart maps a lot ot get a great map, where I've started to set almost all settings to random, to make it more interesting/exciting.