Since Kassadin serves as an anti-mage or, it may be a good idea to choose a physical damage champion against him or any champion that can zone him out before he can access his ult for laning phase since Void Stone only protects him from magic damage. Prime examples are: Talon & Zed. Keep in mind that Kassadin will buy Zhonya's Hourglass against them.
Remember that Kassadin is a champion that is almost uneasy to kill due to his extremely low cooldown of his ult. Crowd Controlling him can shut him down in teamfights.
Another way to shutting down Kassadin is to play a long ranged champion like Caitlyn or Jayce against him.
Any champion that can easily keep up with his Riftwalk movement is the best way to counter him. Prime Examples are: Kha'Zix, Vi & Fiora. however among the three, Fiora is probably the best choice against him for three reasons: First, Lunge can match the cooldown of Riftwalk as long as Fiora hits an enemy with it, Second, Fiora also deals physical damage. and Finally, Fiora is considered the only champion that can keep up with Kassadin's movement in the late game.