For me, the #1 answer is Culture. Not only do I find it the easiest, but also the most fun because I love building wonders and creating fabulous cities.
Second place I guess would be Science. It’s pretty cool seeing those launch animations, but gosh, it sure takes a long time to get there. So much tedium.
It’s usually faster (taking fewer turns) for me to get a Religious victory, but I don’t really enjoy it too much. It’s a drag moving those Apostles and other religious units all over the place, and the AI doesn’t seem to put any serious effort into stopping me when I go in and convert cities. Sure, they’ll complain, but that’s about it.
Probably the second easiest for me is Domination, but it’s not much fun. I dislike all the killing, and it’s a whole lot of busy work getting all the correct units where they need to be.
I finally was able to win a Diplomatic victory a few days ago, which is what prompted me to post this poll because holy cow, what an awful experience that was. I like the idea, in theory, but it’s really badly executed. Others have enumerated elsewhere all the reasons why it doesn’t work, and to save space I won’t go into them here. But it will be a very long time until I try that one again.
As for the Score victory, I’ve never even tried to achieve this, and I’m not sure why I would except to get the achievement in the Hall of Fame. But would that be worth waiting and waiting and waiting, turn after turn after turn? I doubt it.