A classical language is a language with a literary tradition that can be judged as "classical".
According to
George L. Hart:
[To] qualify as a classical tradition, a language must fit several criteria: it should be ancient, it should be an independent tradition that arose mostly on its own not as an offshoot of another tradition, and it must have a large and extremely rich body of ancient literature.
Note that the judgement of a language as "classical" is a judgement of its literature, not the language itself. No language is inherently more "classical" or "ancient" than another in terms of phonology or grammar. Nor is any language immune from change; classical languages therefore tend to be either dead languages, or show a high degree of diglossia.
List
The following languages fit George L. Hart's definition:
See also