America
America remains a solid choice for a nation, able to pursue any type of victory. The +1 Sight bonus of Manifest Destiny can help you spot incoming barbarians and better protect your Trade Routes. Put your eagle-eyed Archers on hills to keep the roads clear.
Arabia
Arabia's new Ships of the Desert passive power replaces their former Trade Caravan and puts Arabia in the spotlight as a dominant trader by land. You'll be able to send your Trade Caravans almost anywhere with a 50% bonus to their range, and they are twice as effective at spreading any religion you choose to pursue. Arabia still gets double Oil, so if you choose to be militaristic, your armored vehicles won’t run out of gas!
Ships of the Desert
Caravans gain 50% extended range. Your Trade Routes spread the Capital's religion twice as effectively. Oil resources are doubled.
Aztec
The Aztecs remain largely unaffected in Brave New World. They remain an early game military powerhouse, able to cope with increased barbarian activity and any neighboring civilizations. If another civilization is becoming too influential, the Culture generated by a good war will help your civilization regain its independence. If the target of the bloodbath is the civilization putting Tourism pressure on you, all the better!
China
China is one of the nations least affected by Brave New World. It remains a powerhouse in every facet, with a strong military and Culture. You won’t be getting many bonuses besides your Great Generals, but you’ll be a force to contend with the entire game.
Egypt
Egypt builds Wonders, and it always will. To further increase your ability to create marvels, set up internal Trade Routes that increase Production in your best Wonder-building cities (likely your Capital). Civilizations pursuing Cultural Victory get very strong Tourism bonuses through Wonders with multiple Great Works slots, so consider building them to work toward a Cultural Victory or simply to deny them to others.
England
Her Majesty’s Navy rules the waves! Overseas trade ships benefit from the protection of the mighty British Navy, or you can use them to hunt down the trade ships of other civilizations. Your enemies won't approach that, but if they want to do anything about it they’ll have to contend with your warships.
England's extra spy helps throughout the mid- and late game. Use them to help with stealing Technology at first, but let them aid your diplomatic pursuits in the final stages of the game. They can help you grab City-States or became an extra Diplomat to increase your voting block. Either way, England benefits!
France
Playing France is for those who love the finer things in life. You are going to have a Capital that dominates the world through Art and Culture. A good war now and again may let you get new territory (and your Musketeers do it in style), but the heart of France will always be Paris and its Great Works.
France has changed substantially since Gods & Kings. They have a new passive ability, the City of Light. And they’ve lost exclusive access to the Foreign Legion, but gained a unique building called the French Chateau.
City of Light
France gains double Tourism from Theming bonuses in Paris from its Museums, World Wonders, and National Wonders.
Chateau
The French Chateau is a new building that provides a small amount of Gold and Culture, with the promise of more Culture and Gold once Flight is researched. Should war come, they provide the same defensive bonus as a Fort, so they've got a practical use in keeping the countryside safe. They have to be built next to Luxuries and can't be adjacent to each other. It’s just not the same if everyone has a mansion, after all.
Establish a solid Cultural base early on, and get started on the path of Cultural Victory. Make sure to use Tradition and Patronage to set up your cultural pursuits. Create a nice, small empire and don't overreach. France's unique unit, The Musketeer, is still a potent force on the battlefield, but it won't be available for some time. In the early game, you'll get stomped by other civilizations that are out for conquest unless you're careful and play defensively.
Your best bet to survive into the late game is to be very cautious in your expansion and only take as much land as you are sure you can hold. Trade is very much your friend, as you'll be able to befriend nearby City-States and keep your satellite cities fed. Once you've got them established, you can start to use them to feed Production back to Paris, accelerating the construction of Wonders in your Capital. You'll want to prioritize World and National Wonders that have two or more slots for Great Works, as the new passive Power of France relies on collecting Great Works in the capital.
Once you've got Musketeers, consider making a small expansive push to maximize the advantage they have over basic Musketmen. If you are sitting pretty on a small Empire that is running like clockwork, stay tight and don't antagonize the neighbors! Your goal is to steadily wear away at their Culture, dominating their hearts and instilling a love of all things French in their souls. You'll start to really see an impact once you reach the Modern age, as you'll start getting buildings that enable you to use Culture to boost Tourism (like the Hotel) and increase Culture on their own (Broadcast Towers). Accelerate the process by exploiting Theming bonuses with your Great Works in Paris. In the end, it won't matter what civilization your neighbors call themselves—they'll secretly long to be French.
Theming bonuses are very complex, and they're explained in the Single Player's Path section. In short, you have to use Great Works carefully in each building because there are bonuses for grouping them in specific ways.
For France, it's essential to make Paris a center of Culture for your empire. Their Tourism potential is amazing. Use Aesthetics to give yourself the best bonuses, and watch the world come to you.
France no longer lays exclusive claim to the Foreign Legion. Now, they can be trained by anyone who takes the Volunteer Army tenet of the Freedom Ideology. In practical terms, this isn't much of an impediment to a Culture-heavy civilization. The Freedom line is a good one for France, as it focuses on Culture and Tourism, so there is very little reason not to invest in it.
Germany
There are slightly more barbarians in Brave New World, so practice your maniacal laughter as you contemplate all the extra units that can give you. The German civilization has always been a strong military nation, and this just makes them even stronger in the early game.
Greece
Cementing Alliances with City-States has always been a good idea, and now they can give you even more weight diplomatically. This helped for winning the game before, but it didn't do much for you before reaching the final push to the end. Now it does. City-States give you votes in the World Congress, making life better for you and often harder on your enemies. Greece should use their passive bonus and Patronage to establish a strong presence on the world stage.
Send Trade Routes to City-States to start getting them on your side, which will also make money you can use to wean Alliances away from other civilizations with well-placed bribes.
India
Because settling new cities causes your Happiness to plummet, India is a good candidate for staying defensive and going for a Diplomatic or Cultural victory later in the game. Your Mughal Forts now boost Culture rather than Gold. Use this to get Policies sooner and to resist the Influence from other Cultural nations.
Iroquois
Like before, if the Iroquois can start in a large enough forest, they’ll be able to make good uses of their inherent bonuses. This extends to Trade Routes, as the ability to move through the forest quickly helps their Caravans get where they need to be unmolested.
Japan
Japan is almost completely unaffected by the changes of Brave New World. Let enemies beware even the most wounded Japanese unit, as they continue to fight until their last drop of blood is spilled. Seriously consider the Autocracy Ideology; it makes Japan's military quite worrisome to engage.
Ottoman
For fun and profit, raid Cargo Ships for quick money. You’ll earn enmity from your fellow civilizations, so have a backup plan when the life of a pirate turns sour!
Persia
The Golden Ages of Persia continue to be their strongest times, during which they expand and conquer. The Satrap’s Court now provides even more Gold than a regular Bank as well as all the Trade Route perks of having a Bank in the city, so build one every chance you get. Amass your wealth in between ages and then use it to expand when the Golden Age dawns.
Make sure to construct an Artists' Guild as soon as possible, in a city with a proper Garden and a National Epic. Persian Great Artists let you control the dawning of Golden Ages; trigger them with your Great Artists at the beginning of each war and watch your foes melt before you. As in Gods and Kings, pursue Chichen Itza as well. The combination of frequent and longer Golden Ages is impressive—doubly so for Persia.
Rome
All roads lead to Rome! You’ll want Rome to have a wide variety of buildings to get the most out of their passive power. Make sure to use your satellite cites as Trade Route bases and create Production for Rome by establishing internal Trade Routes. You’ll be able to construct buildings in Rome at an accelerated pace, which lets you build them in your surrounding cities at an accelerated pace as well.
Russia
Russia endures the changes of the Brave New World with a grim determination and remains largely unaffected. You’ll be able to pursue any style of play, and the extra resources are useful when war inevitably comes.
Siam
With the added emphasis of Culture and Diplomacy in Brave New World, Siam is a great choice if you are seeking a peaceful game focused on winning a Cultural Victory. Because you make friends with all the City-States you find, you’ll likely be a powerful voice in the World Congress. Manipulate Resolutions to provide the maximum benefit for your Culture. Make sure to get along with your more warlike neighbors through Trade Routes, and if they start eying your territory, cut them off or use the World Congress to undermine them diplomatically. Embargos against enemies, Standing Army Taxes, and Nuclear Weapons Bans are all in your favor.
Songhai
The increased barbarian activity provides fodder for your empire, so go out raiding as soon as possible. You’re likely to be less dependent on trade than other civilizations, so fund your activities and cut off their resources by plundering their Caravans and Cargo Ships.