The language of the Elder Scrolls games is known simply as The Common Tongue. It is sometimes referred to as Cyrodiilic or Tamrielic. It is almost universally spoken.
Morrowind has the additional traditional minority language of Dunmeri, which is used mostly in place-names but also in slang and quotes. (see http://www.imperial-library.info for Dunmeri dictionary.)
Other Elder Scrolls languages are the one used in the book N'Gasta! Kvata! Kvakis! - actually
esperanto! - and the old Ayleid language, Aldmeris:
Aldmeris is the original Elvish language, still spoken as a first language among isolated Elven communities, and spoken and written by all educated Elves, and the language of the Elven arts. The root '-mer' is anologous with the root '-man' or '-men' in human language; thus, the Elves are mer as Humans are men.
NB, the Dwemer language is a dialect of Aldmeris, but mostly untranslatable.
Daedric, as used in Morrowind/Oblivion, is actually a script rather than a separate language.
http://www.imperial-library.info/daedric/