I'd imagine the Ashlanders, Argonian tribes, Khajiiti desert tribes, and Alik'r nomads still speak their own languages. There is no logical reason for any of them, besides their leaders, to understand any other language. They weren't really conquered, and pay no attention to Imperial law.
But wouldn't all mer speak the same language, considering they are all descended from the Aldmer? Different dialects, sure, but probably the same root.
Then you've got the Nedes - they came from Atmora, right? So, the proto-men had their language, and the Nedes differentiated into the Nords, Bretons, and what is now collectively called the "Imperials." The Redguards (or, rather, the Ragada), definitely have their own language, since Cyrus needed Coyle to translate Coyle's mom's Yokudan.
I'm sure the Argonians probably have their own language - they are so unlike the other races, it is probable that they also have their own language.
In TESIV, it seems the Ayleid have their own language for at least magic - is that ancient Aldmeri, though?