The shortest game lasts only 3 seconds. But it is modded. Start on a land with only mountains. When you start, just press enter and all other civs, seeing there is no land to settle, disband there settler and die. You're the last one standing -> conquest victory in 3950 BC. And a very high score, but very limited game-pleasure.
The longest: well, we are currently playing a game where 10 turns took about 18 hours. It can last as long as you want.