Here's my big list of Civ Balance:
Overpowered:
Persia
Arabia
Portugal
Persia is always among the top five civs from the beginning to the end. They should be a strong ancient power, but begin to fall back after the late ancient age. Portugal almost always ends up outdoing Spain, and I've even seen it extend into France. They also tend to do well because some of the Arabia has a beautiful site for Mecca, and it also gets pretty much all of the Islamic wonders. It also has a scout and plentiful huts, so it almost always gets an extra city to start. These combined factors make it fairly formidable.
Just right:
France
Austria
Scandinavia
Rome
Netherlands
Russia
Israel
Carthage
Zulu
Ethiopia
Babylon
Mongols
Japan
Korea
Aztecs
Iroquois
Incas
These civs are all fairly well balanced. However, I have a few criticisms. The Scandinavians tend to have roughly the right amount of power, but I think it would be better if their power was shifted earlier in the tech tree. They should peak in the early middle ages. However, it usually takes them a while to fill up the Scandinavian peninsula, so their advantage is later on in the game than it should be. Also, Babylon remains powerful for a while longer than it should. It should begin fighting an uphill battle by the late ancient age. Lastly, the Mongols seem to do a little too well. I've seen them enter the industrial age at the same time as the tech leaders. They should grow large and they should be pretty formidable in the Middle Ages, but they should fall behind midway through the second era.
However, most is really good here. France, Russia, and Austria can all sometimes dominate a game and sometimes do only average. The Aztecs, Iroquois, Incas, Ethiopians, and Zulus are powered about right as well. They're somewhat crippled, but not total pushovers. Israel, Korea, and the Netherlands are all capable of doing well, but generally don't, which is good.
Need a little boost
England
Germany
America
Ottomans
Byzantines
England, Germany, and America should all be top-tier civs, and unfortunately, they often aren't. Germany is pretty weak in comparison to its neighbor, France. IMO they should be about even. Just a tiny boost would help them a lot. England can do well if it makes it to the industrial age safely, (it gets some new resources then) but it's often too far behind by that time. England needs some help before then. Real life England was probably the single most powerful civ on Earth for several centuries, starting in 1588, when they defeated the Spanish Armada. I think some earlier boosts would let England be as powerful as they should be. America is about the right size, but it's generally too far behind by the time it's discovered, and it can never really recover to build the Statue of Liberty. I think they should be boosted not in sheilds or food, but in trade. They grow big enough, but they fall behind in tech. They should be able to make a better comeback. Lastly, the Byzantines and Ottomans basically weaken each other. I'm beginning to agree that one of them has to be removed. There just isn't enough space. But if we have them both, they have to be helped a little.
Underpowered:
India
Maya
Spain
China
Greece
Egypt
The Maya stand out as the single most hopeless civ in the game. In my three most recent games, they've never had more than two cities by the time the Americas were discovered. They certainly shouldn't build a big empire, but right now they're pretty much pointless. The Aztecs generally grow to three times their size and often beat up on them. It's just not fair.
India and Spain should do fairly well sometimes. But they don't even come close. India should grow large and have a high population. But in almost every game I see the Ethiopians and the Zulus surpass them in population. Make the Sacred River wonder more powerful, or give them a cow to start or something. Spain is also too weak. I have seen several games where they don't establish a single colony(!). They should establish more colonies than any other European civ. They fall behind because Portugal always takes the Iberian goody huts with its scout and out-expands Spain.
China and Greece should be better than they are right now. In RoC China was too good. Now I think they aren't good enough. They're always behind in tech. Greece, too, is way too weak for their real life power. I think it's mostly because the Byzantines crowd them too much. Generally the Byzantines found Adrianople to the north of Greece, so Greece can't have a connected empire of more than two cities.
Lastly, Egypt is always weak. They should be weak beyond the ancient age, but as it is, they're not even powerful in the ancient age. I think the Pyramids should be fairly cheap, so that they're the first wonder built more often than not. That would help Egypt a little. Also, it couldn't hurt to give them a little more food and sheilds.