My three favorites are Polynesia, France, and England, although I'm also partial to Byzantium and Korea. I imagine I'd like Brazil if I played them more. I like maps with plenty of water, and Continents Plus or Terra are the earthiest I'll take. Even then, I tend to turn up the water level (and make it 3 Billion Years Old - mountains are pretty!)
Polynesia is an oddball choice, but they're perfectly suited to my playstyle - I love to build beautiful empires. Building plenty of Moai means I can expand to any spot I want anywhere on the map and keep the social policies coming, and once they start producing tourism a Cultural Victory is coming in short order. Their early embarkment means a bunch of free ruins, and it has the surprising tactical advantages of being able to "retreat" into deep water and travel the seas completely invulnerable to attack until Astronomy, at which point a navy can escort your troops. The embarkment bonus applies to triremes too, making them incredibly useful explorers. The Maori Warrior is not incredibly inspiring, but it gives you the edge against barbarians you need in the early game and the defense you need to defend far-flung settlements from attack. Plus, they're so much fun to play on Terra or Earth (especially if you make a beeline for Australia).
France has become my newest favorite after BNW. I love theming bonuses and I love seeing France's massive inflated City of Light tourism. I'm a sucker for UI, especially cultural ones, and chateaux are just so darn pretty. I also happen to really enjoy the flair of unique musketmen, and the Musketeers have flair out the wazoo. Vive la France!
England is my go-to when I want to conquer the world and make them scream, "Hail Britannia!" England is great because, as I've mentioned, I love water and no one moves around in it better than England. More importantly, they're the only Civ in the game with 3 UU's. As soon as you get bored with one, the next one comes along. First, you get Longbowman, my favorite UU - crossbows with the potential range of Artillery are so very cool, even if you can't shoot to your full potential most of the time. You can start your conquest in the middle ages with them, and as soon as you get bored, Ships of the Line come along to keep the slaughter going. Once you start rolling your eyes at them, along comes Industrialism, and all your promoted longbows upgrade to Gatling Guns with 2 range - your unofficial UU and arguably the most powerful. And all the while, your extra spy is filling in the top of the tech tree while you murder your way through the bottom.
As for Byzantium, I love the religious game, and building a super-religion outweighs the "quirkiness" of their early UU's. Besides, I like the dromon and come on, it breathes fire, and cataphracts are actually quite useful as super-mobile city-takers when combined with catapults. My favorite way to play Korea is actually Kultural, going down Piety, focusing on GWAM specialists, getting Messiah as an Enhancer, and planting plenty of great prophets. It's certainly suboptimal, but it's a lot of fun.
Figured after 1000 hours played and many hours reading threads here that i'd actually start to post eh!
and capitol 
and beautiful Polders once the right era is reached. i feel like Netherlands is easy to turtle with but you can turtle and win with any civ. just that this civ feels like you're playing a level below the actual level. unless they start you with no Marsh.
