The greatest champs globally to counter Karthus include Kalista, Lucian, and Aphelios. These are all great at countering Karthus with decent win rates over 62%. Even if these Karthus counter picks are not chosen in the same position as you, it's not smart to take him into these matchups. They will most often win against Karthus.
Conversely, if the opposite team picks either Taliyah or Xerath, you should seriously think about choosing him, as he easily destroys these champions with win rates over 54% against both ofthem.