We study (1 + 2)-dimensional equivariant wave maps to a surface N. These are, after reduction, solutions u : ℝt × ℝr → ℝ to the following initial value problem: utt − urr − (1/ r) ur = − f(u)/r2, (u, ut)|t=0 = (u0,u1) (f depends on N). We consider the existence of a finite energy harmonic map Q (a stationary solution), and show that when it exists, Q is unstable in the energy space. Our result applies in particular to the case of wave maps to the sphere S2, and to the critical Yang-Mills equations in dimension 4.