Originally Posted by Beaumains
I wouldn't say there are too many hard counters to Karthus in mid. There are a lot of highly challenging opponents mid (Ori, Lux, Kat, LB, Kass, for example), but they do have counterplay and it is possible to get the upper hand on them, especially Kat.
Those plus any assassin type champions. I would add Ahri to the list above. Other nonconventional hard counters I feel to include would be Akali, Talon, AP Trist, Ezreal, Pantheon, Fizz. Granted these are just from my experience.
I realized I may be using the term "counter" a little too loosely in which case I'd agree with your terminology of "highly challenging opponents with counterplay."