We find the explicit forms of the anti-de Sitter plane, anti-de Sitter spherical, and pp waves that solve both the linearized and exact field equations of the most general higher derivative gravity theory in three dimensions. As a subclass, we work out the six-derivative theory and the critical version of it where the masses of the two spin-2 excitations vanish and the spin-0 excitations decouple. © 2015 American Physical Society.