What *isn't* Typeable in GHC 7.8?

I'm working with the author of syntactic to add support for a wide variety of types. I proposed using type lists to allow any type to be used, the dev proposed a cleaner solution that allows use with any instance of `Typeable`. I know (at least the current version) of `Data.Reflection` doesn't support `Typeable` reified types in GHC 7.8, but at least they proposed a workaround using `lens`. My question is about the original proposal for the library: aside from (some forms of) reified types, what other types in GHC 7.8 cannot be made an instance of `Typeable`? If these types are sufficiently strange/rare, it could suffice to use the clean solution that requires `Typeable`, but if there are [other] commonly used types that aren't `Typeable`, the type list would be the more general solution.