Existing limits on the nonradiative decay of one neutrino to another plus a massless particle (e.g., a singlet Majoron) are very weak. The best limits on the lifetime to mass ratio come from solar neutrino observations and are tau/m greater, similar 10(-4) s/eV for the relevant mass eigenstate(s). For lifetimes even several orders of magnitude longer, high-energy neutrinos from distant astrophysical sources would decay. This would strongly alter the flavor ratios from the phi(nu(e)):phi(nu(mu)):phi(nu(tau))=1:1:1 expected from oscillations alone and should be readily visible in the near future in detectors such as IceCube.