Depends on what victory condition you tend to play for. For some people who like to keep things random, you won't always know how you'll win the game, so it's hard to say exactly. If you had to break it down by strengths, I'd say:
For science, Babylon or Korea. Neither are particularly good at domination, but having a solid tech lead helps in conquest.
For domination, Mongolia, the Huns or Persia. Mongolia and the Huns are all about their UU. The Huns are stronger earlier and taper off, while Mongolia can use its UU for a surprisingly long time. Persia's strength is getting Chichen Itza to combine with their UA and having 20(?) turn Golden Ages. During Golden Ages, Persian units get +1 movement and +10% strength, which lets you move over hills and rivers and attack on the same turn. There is also a group of World Wonders late in the game that can give you 4 Golden Ages, plus the ability to buy Great Artists with faith, so you can stay in a Golden Age indefinitely.
For culture, Persia is a good choice. I think culture is heavily dependent on what difficulty you are playing at. At Prince or lower, I doubt you need Egypt's UA to help you build wonders, whereas at higher difficulties that 20% bonus might be the difference. France is good for its +2 culture per city bonus, since it helps you kickstart your empire faster. India might have been a good choice originally since you need to go Tall in order to get a culture victory anyway, but in G&K I don't think you'll have much trouble with happiness using a 4-5 city/wonder heavy strategy.
Other civs can be strong depending on the circumstances (Spain starting near a good natural wonder, like Uluru or Mt. Sinai).