I always play on normal speed. Game length however depends upon map size. I'll handily win a domination victory on a small map around turn 200-250. For standard map sizes, actual victory usually comes between turn 350-400. Usually however, I stop around turn 250, because at that point the computer has no hope of defeating me (and especially playing multiplayer, OOS's strike fairly regularly around that time). Note, I usually end up going for a domination victory, though often I'll look at the score, realize that I control 60% of the world population, but 40% of the land area, and then race between finishing a domination victory and smashing out an altar/cultural/ToM victory. Usually, domination wins... I could of course go for conquest, but I hate leaving all that wide open land...
-Colin