Austria
Diplomatic Marriage is a wonderful option for getting new land for your Empire, but there is a downside. Allied City-States provide an extra vote in the World Congress, but Annexed or Puppet City-States do not. If you want to rule the world as an elected leader, think carefully before buying out all of the City-States!
Byzantium
The Byzantines remain a religious powerhouse, and Trade Caravans spread your religion wherever they go. Send out the tenets of the faith with your Trade Routes, and rake in Gold in the process. In addition, look for some of the new Wonders that provide missionaries or increase religious pressure from the Capital to make sure that yours is the one true Faith.
You were likely to take all of the Piety Policies anyway, as a Byzantine player, but really work on them now. They're awesome! The final Policy lets you choose a bonus power for your religion, and the list is filled with powerful options for multiple styles of play. You can't go wrong.
Carthage
Traders should absolutely rejoice, since Carthage’s free Harbors increase the Gold of your overseas Trade Routes and the distance your Cargo Ships can travel. Their mountain-crossing power is situationally useful, but everyone could use more money!
Celts
If you are going for a Cultural Victory, you get some benefit from the increased Faith generation of the Celts, as it helps you buy great Artists, Writers, and Musicians, and the Ceilidh Halls improve your Culture.
Ethiopia
Ethiopia is a strong nation that is excellent at creating and then defending a small Empire. You have a good shot at lasting until the late game and going after the longer-term Cultural or Diplomatic Victory, especially if you dedicate to that goal from the start.
Huns
Trade, Culture, and Diplomacy are for people who don’t have the courage to ride with Attila’s Horde. Let them plot and plan for a late game that will never come. As with many warmongers, the Huns don't change their strategy much in Brave New World.
Maya
The Mayans are an odd bunch that can be taken in any real direction. They excel at getting a religious edge early on, so you’ll be able to start putting religious pressure on your neighbors through trade from the start.
Netherlands
The Netherlands are an excellent choice for a dedicated trader. They do best on the sea, but anywhere there’s money to be made through the exchange of goods, the Netherlands will make a profit.
Sweden
Sweden is one to pick if you want to use the World Congress to change the world to your liking. Their ability to sway City-States to their side means that they’ll have the votes they need.