For some games, when I'm clearly going to win, I'll quit rather than play it all out. I'd rather move on to a new challenge, I suppose. However, if I've for some reason had a spectacular game, I will play it entirely. Maybe it's to see the final score, but I think more often it is to see how early I can close the win.
At the same time, I find myself intrigued with games that I'm sure I can no longer win and the situation for my civilization is tenuous, usually just at or below mid-field but with dangerous enemies about. I'll play some of those through to the bitter end, just to see if I can survive or, more rarely, make a surprising underdog comeback.
I wonder, do any of you tend (like me) to play the same leader/civ for a series of games? I find that I almost always fixate on a strategy and then pick a leader that seems most suitable for it. I then iterate the strategy over many games, 10+ at least. Just as often, that ends up with a new derived strategy, a new leader choice, and a whole other row of games played in the same fashion.
It has led to me being able to play some leaders on higher levels (for me at least), even leaders some would consider arguably weak (such as, say, Saladin), but virtually incapable of playing other leaders whom I haven't ever focused on much, even if they are stronger.
This also leads to situations where I'm in the "underdog" position at a tougher difficulty, but I'll play it out because I feel like I have at least a slim chance with a familiar leader that I've proven an ability to play with in the past. Curious, I never really considered that as a possible reason why I play out some "loser" games, until this thread had me analyze my playstyle a bit more.