I encountered one condition where calling get_type_hints causes infinite recursion when dealing with forward declaration and cyclic types.

Here's an example:

from typing import Union, List, get_type_hints

ValueList = List['Value']
Value = Union[str, ValueList]

class A:
    a: List[Value]

get_type_hints(A, globals(), locals())
This reaches the recursion limit as of 3.8.0b2.

It seems that the combining _GenericAlias with ForwardRef is what triggers this condition:

ForwardRef._evaluate sets __forward_value__ on its first call on a given instance
_GenericAlias tries to compare its args post evaluation
If one of the arguments is a previously evaluated forward reference containing a cycle, then it will infinitely recurse in the hash function when building a frozen set for the comparison.
The above is, of course, a very artificial example, but I can imagine this happening a lot in code with trees or similar structures.
My initial reproduction case was using _eval_type to resolve forward references returned by get_args (side note: it would be nice to have a public function to do that).