The frequencies and damping times due to (bulk and shear) viscosity and gravitational radiation reaction are computed for the lowest frequency 0≤l≤5 modes of a wide range of nonrotating fully relativistic neutron star models. These computations generalize previous results by determining the effects of bulk viscosity (using coefficients appropriate for normal matter, pion-condensed matter and strange quark matter, respectively), by examining a large set of modes (including the radial and dipole modes), and by expanding the sample of neutron star matter equations of state. These damping times play a crucial role in determining the stability of rapidly rotating neutron stars (in effect determining their maximum angular velocities) and in any model of periodic astrophysical phenomena that involves a pulsating neutron star.