IO and ST
Many primitive types, including unboxed tuples and State#
mtl
newtype Fix f = Fix (f (Fix f))
data Tree a = Leaf a | Bin (Tree a) (Tree a)
data Foo a b = a (tests proper defaulting behavior)
A type family from my old TrieMap package with kind -- I kid you not -- ((* -> *) -> ((* -> *) -> * -> *) -> (* -> *) -> * -> * -> *)

Things that it will not work on, and that I don't think will change:

GADT types that cannot be reified by TH. Essentially, I think this is "the set of GADT data types that actually couldn't be implemented without GADTs." Not sure, though. In any event, at the moment, I don't think there's any hope of handling GADTs in TH at this point, so I don't really object to this problem.

Anyway, y'all should attempt to break th-kinds. Tell me if you can construct a type for which my inference checker breaks, but not because you get an error message saying "Can't reify a GADT data constructor..."

By the way, I'd like to bump these tickets. They're certainly related, but I'm not sure if they're genuinely equivalent. It's really irritating, though, that kind parsing is so broken in TH, and I think that a TH backend guru should be able to figure out where there's a foldr instead of a foldl... th-kinds includes a workaround to this bug, but if the bug is fixed, it'll break again. Yuck, bugs.