First, another question would be on the leaders. As there are civilizations that deserve more than one, (e.g. an easy way to represent both the Brits and the English, both of which are worthy of inclusion, but not at the same time), it is a question not to forget!
But if you ask just for the civs, here is my list:
Core
America: No matter how much you discuss it, they deserve inclusion!
Arabia: A very big people with big influence on history
Aztec: Classy, it's a civ evergreen.
Babylon: Same as above!
China: It is that large it'd deserve more than one civ, but that's sadly not possible
Egypt: Don't count the millenia of years of culture, it's just too much
England: English is the modern world language. The Problem with Britain is avoided by adding leaders from both eras and "merging" Scotland, Ireland and others with the Celts.
France: Hegemonial power of most of Europe's History, pressing its culture into everything, being it Absolutism or the French Revolution.
Germany: Slightly a opposite of France, this people is important (From HRE to WWII)
Greece: The basis of our Western civilization and although quite exotic, it is in, both with aggressive Alexandrian Hellenism and City-state democracy.
India: not thinkable without.
Japan: it squeezes itself in
Mongolia: With it's half seat and China's other one, it just gets inclusion.
Persia: Alexander needs someone to conquer.
But it is also one of the few countries with a continuing history, don't forget the Shahs of Isfahan, Rai and the Ayatollas of Teheran.
Rome: Define Civilization: Rome!
Russia: From St. Petersburg to Wladiwostok, the Russian Winter awaits you.
Turks: If you think Ottoman, yes, but also don't forget the Seljuks and the other Turkmenic tribes.
First expansion:
Celts: Not only the Gauls, but also the Gaelics, mix it somehow and better than as in civ4 (Bibracte was a Humiliating defeat, not even a great one, and certainly no big city! Why don't they take Alesia or Gergovia?)
Inca: More Worthy than the Aztecs, but popularity counts more.
Spain: Also I am very sorry not to have put you in into the core game.
Carthage: Classic Civilization Civ.
Mali: improve Africa, Yeah!
Poland: This one is so many times just overlooked and I really need to make a case for their inclusion. How many Slavic civs do we have? and how many Germanic/Romanic (Western Europe) ones? It's history with the partitions is unique, interesting and it just fills the gap.
Second Expansion:
Khmer: I think the Khmer have more flavour than the Thai, imho.
Maya: Astrology mysteries, always interesting
Assyria: It has a hard time besides Babylon, but I think we can include it.
Scandinavia: Not the vikings!
Iroquois: Better than the Sioux and nevertheless native American.
Korea: I have a hard time deciding between Korea, Austria-Hungary (both as one civ!) and Ethiopia (no Zulu!). rating: 1. Korea 2. Ethiopia 3. Austria-Hungary
I didn't include the Netherlands and Portugal due to the reasons that they are quite specific civs that do not add cultural variety (in comparison to Mali, Korea, the Khmer or the Scandinavians). Holland is a own culture , but - sorry to say - it is kind of a mixture between Germany (look at the language and history), England and France. Its greatest achievements are shown/included as European Colonialism with England and France. It is the same with Portugal, no place besides Spain, I'm sorry.
A few words to the other lists:
@skippy_T You think Bismarck is no worthy leader? I advise you go read something on him, he managed to fool all of Europes top diplomats when he was in office grabbing a "place under the sun" for Germany in the top league. When he went, Germany declined and lost many of his gains which ultimately ended in World War I, and we know what that ended in.
The Old Fritz (Frederick II. of Prussia) on the other hand is the classic leader guy. Diplomatic Genius, a good "general" and really educated.
@magritte that's just weird. Your creating not the game "Civilization", but rather "Social Evolution" or something like that.
@Thedrin Including the Habsburg is somehow genius (as you can merge some cultures into it), but it's definitely a totally different way than all the other civs (you mentioned), and that's why it doesn't work.
mfG mitsho