Each civ has a Unique Weakness to balance its Unique Power. Simples.
Americans - Homeland Security
If an enemy Spy carries out an espionage action, -10 unhappiness in that city for 3 turns.
Arabs - Café Culture
Coffee reduces the effectiveness of Barracks, Security Bureau and Intelligence Agency by 50%.
Aztecs - Omen of Quetzalcoatl
When conquerers appear, random Aztec units defect (as in a War of Liberation).
Babylonians - Epic of Gilgamesh
Improvements in flood plains randomly destroyed.
Byzantines - Iconoclasm
Classical, Christian, and Zoroastrian Wonders cause -1 unhappiness.
Chinese - The Chinese Character
The civ cannot research Alphabet themselves; they have to get it from trade.
Congo
Dutch - Hilversum Tolerance
Broadcast Towers also increase the culture of random /other/ civs in the city.
Egyptians - Al-Jazeera
Your stability is reduced if you research Satellites or anyone else completes The Internet.
English - Cuppa
After Astronomy, -3 happiness in any English city that does not have access to Tea.
Ethiopians - Beta Israel
When you build your first Airport, that city loses a population point to Jerusalem.
French - Pétain Effect
If they lose five units in a single turn, they capitulate to their most powerful opponent.
Germans/Austrians - Hap-py Families
For every ten turns the civ is in Dynasticism, -1 health and -2 stability.
Germans/Prussians - Banking Crisis
If the Single Currency resolution is passed by the UN, then the German treasury empties and -2 unhappiness in all cities.
Greeks - Banking Crisis
If the Single Currency resolution is passed by the UN, then the Greek treasury empties and Banks have no effect.
Incas
Indians - Bollywood
If other civs trade Hit Movies or Hit Singles to you, then they have no effect.
Indonesians - Pancasila
Chinese culture in your cities causes extra unhappiness.
Italians - Berlusconi Bungs
Broadcast Tower increases corruption in the city by 50%.
Japanese - Otaku
When Computer Industry are present in a Japanese city, productivity declines 10% but +2 happiness. +1 more happiness if the Seafood Industry is also present.
Khmer
Koreans - Juche
If the civ is Totalitarian+Supreme Council, then it has -5 relations towards all other civs.
Mandi - Gold Lust
If a Mandi unit moves onto a tile with Gold, then it cannot move again.
Maya - Mayan Calendar.
If you play as the Maya, the game ends in 2012.
Mongol - Lamb Kebabs
Pig and Cow cause unhappiness, offset by extra happiness from Sheep.
Mughals - Taj Mahal
If the Taj Mahal is built, all the other cities have -1 unhappiness.
Persians - Press TV
The Internet has no effect.
Phoenicians - Carthago Delenda Est
If you lose a city in your Core Area, it is automatically razed.
Poles - World History Forum
The history display at the end of the game may exaggerate Polish influence on the map.
Portuguese - Angolan Currency Scam
If Portugal has any cities in Africa, inflation increases by 10%.
Romans - Lead Pipes
Aqueducts reduce science output by 20%.
Russians - Conscript Hazing
Newly conscripted units immediately take 20% damage.
Spanish - Mañana
Spanish units occasionally have their movement points set to zero at the start of a turn, rendering them inactive.
Tamils
Thai - R&R
Foreign military units in Thai cities cause -2 health.
Tibetans - Monkery
Buddhist Missionaries cause -1 unhappiness when present in a city.
Turks - Enosis
Greek culture in Turkish cities causes triple unhappiness.
Vikings - Snus
Tobacco causes -2 health in Viking cities.
Can anyone help with the missing civs? The list of omissions is sadly predictable; I wish I knew more about those peoples.