With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with a lossless impedance boundary. With increasing size, these multipolar resonances are damped and shifted with respect to the magnitude of the surface impedance. The electric-type resonances are inductive and the magnetic ones capacitive. Interestingly, these subwavelength resonances resemble plasmonic resonances in small negative-permittivity scatterers but occur in two families unlike the only-electric multipoles in the plasmonic case. The fundamental dipolar mode is also analyzed from the point of view of surface currents and the effect of the change of the shape into a nonspherical geometry. For dissipative impedance scatterers, maximum absorption is shown to result in the matched-impedance case.