We report the experimental and numerical observation of oscillatory switching between counter-propagating light beams in Kerr ring microresonators. This effect well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Self-switching of counterpropagating light is robust for realizing controllable, all-optical generation of waveforms, signal encoding, and chaotic cryptography. Phys. Rev. Lett. 126, 043901