We discuss how proposed supernova neutrino detectors could measure masses for or neutrinos in the range of 15 to 50 eV. The range for measurable masses might be extended down to 5 eV, depending on our confidence in some of the predicted features of the supernova-neutrino-burst signal. We discuss the expected characteristics of supernova neutrino signals in proposed neutral-current-based detectors. © 1994 The American Physical Society.