In League of Legends, the best counters for Ryze are strong attack damage characters, such as Garen or Riven. Since Ryze is an ability power based character, he is weak against attack damage and anything that can prevent him from casting.
Garen is a good counter for Ryze because his high magic resist coupled with courage lets him ignore most of Ryze's offense, and his Decisive Strike allows him to close quickly with Ryze and silence him. Riven is another good counter for Ryze because her Valor and Ki Burst combo let her close suddenly and stun Ryze preventing him from using his ability's. Her Broken Wings ability lets her overwhelm Ryze with damage.