Civs on the list above that have not been mentioned yet that I feel are under rated are:
Russia - The early production boost is very nice. The extra hammers on horses and iron help produce more when it matters the most. Getting double quantity is also very helpful, you can trade some or you can make more than the others. Double nukes? Yes please.
I get a lot of plains and river starts with them which helps production. The Cossack is better than normal cavalry with the bonus versus wounded units both stacking with the charge promotion and sticks with you when you upgrade to tanks. The Krepost helps expand your borders faster saving you money especially if you do not take tradition and its super expansion.
America - A river start bias helps with early growth when it matters the most. The extra sight helps scouting and warfare. The cheaper border expansions are very helpful in a non tradition game. The minutemen get a free promotion, no terrain cost movement, faster golden ages and everything sticks when promoted? Sounds pretty great to me. Does anyone know if it double stacks with Alhambro for two free rough terrain promos? The B-17 with the extra promos can start with air repair without needing Autocracy or Brandenberg. It might be late but it rocks. it also sticks when it upgrades.
Morocco - Desert starts can be godly with enough river flood plains and hills. If you can get Desert Faith or Petra you can really dominate. The Kasbah makes every desert better, with Petra it makes it almost unfair. The trade bonus can be great with the extra science from being behind in tech on higher levels. The Berber Cav is cav that has a big bonus in home territory and a huge bonus in desert, both of which stick when upgraded. See what Berber promoted into tanks can do. Morocco without desert is pretty useless.