Depends on what kind of war it is. If I'm simply out to conquer that civ and assimilate it into my empire, I'll most probably will simply finish them off. If it's more limited war of acquisition - I may be cleansing my continent from unwanted AI footholds, or be out to occupy a given island - I'll accept peace after securing my objectives, while obviously also taking whatever gold/techs/resources they may be willing to trade for peace. If it's a defensive war, well, destroying the enemy wouldn't be an option (if it becomes, it's no longer a defensive war).
Addition: Note also that if you accept peace with a civ reduced to 1-3 cities, chances are pretty high they'll enter a Military Alliance against you before the twenty turns have passed. Suicidal, the AIs are. This makes leaving them alive for a while more attractive, but for some reason AIs about to vanish entirely rarely has any techs I don't have.