Aquilonia - medieval france
Nemedia - ancient roman empire?
Corinthia - greece in its antiquity?
Pictland - the wild west
Vanaheim/Asgard - vikings, without the drakkars
Stygia - mystical egypt
Vendhya - mystical india
Khitai - ancient china?
Hyrkania/Turan - the mongolians/huns under their great leaders?
Aquilonia represents medieval North Western Europe. It has the army that real medieval kings could only dream of: French heavy cavalry, English longbowmen and Swiss pikemen all in one force. You could conquer the world with that...
Nemedia is a more centralised and romanised Holy Roman Empire of the Germans, complete with Landsknecht.
Corinthia is not very well detailed in Howard. If Rogues in the House is set in Corinthia, it looks like north Italy.
Pictland is indeed the wild west, Stygia, Vendhya and Khitai are Egypt, India and China (in as much as they are detailed at all, and bearing in mind Vendhya isn't all of India).
The Hyrkanians are the steppe peoples, mongols and huns.
The Turanians are the Ottoman Turks.
In addition:
Zingara: Spain
Argos: The naval aspect of England (Bossonia being the other side)
Shem: Ancient Mesopotamia/Medieval Syria
Ghulistan/Zhaibar pass: Afghanistan/ Khyber pass.
Barachan Isles: Carribean (Pirate aspect rather than colonies)
Tortage: Port Royal
Black Kingdoms: Africa
Koth: Holy Roman Empire played rather straighter.