I'm bored and love discussing this stuff. So here's a list of historical capitals for each civ, based on what was the most prevalent capital in that culture's history, or when that culture was at its peek of power:
Japan - Kyoto
Mongolia - Karakorum
Korea - Seoul? (I don't know much about Korean history.)
China - Chang'an then Luoyang (both Han and Tang), Kaifeng then Hangzhou (Song), Beijing (Yuan, later Ming, Qing, PRC)
Siam - Ayuthai
Polynesia - Mu'a (Tongan 'Empire')
India - Pataliputra (Maurya and Gupta)
Persia - Persepolis, Pasargadae, Susa, Ecbatana (The Achmaenids where noted for having multiple capitals for different functions/times of the year - I think that was even their special ability in RoN). Ctesiphon (Sassanid)
Babylonia - Babylon
Arabia - Medina (Rashidun), Damascus (Umayyad), Baghdad (Abbasid, with an interim in Samarra), Cairo (Fatimid)
Ottomans - Bursa and Edirne (early), Constantinople (not Istanbul)
Greece - Pella (Macedon)
Rome - Rome
Spain - Burgos, Toledo, Valladolid (Castille), Zaragoza (Aragon), Madrid (united Spain)
France - Paris
England - London
Germany - Berlin (Brandenburg-Prussia/2nd Empire), Aachen, Frankfurt, Regensburg (sort-of capitals of Holy Roman Empire), Vienna (Austria)
Denmark - Copenhagen (since high middle ages)
Russia - Moscow (Muscovy, Russian Empire), St. Petersburg (Czardom)
USA - Washington
Iroquois - Onondaga
Aztecs - Tenochtitlan (leading city of Triple Alliance. Speaking of which shouldn't those be the first three Aztec cities?)
Incas - Cuzco
Egypt - Memphis (Old Kingdom), Thebes (Middle and most of New Kingdom)
Songhai - Gao