  We study the constraints on neutrino masses that could be derived from the
observation of a Galactic supernova neutrino signal with present and future
neutrino detectors. Our analysis is based on a recently proposed method that
uses the full statistics of neutrino events and does not depend on particular
astrophysical assumptions. The statistical approach, originally justified
mainly in terms of intuitive reasoning, is put on a more solid basis by means
of Bayesian inference reasoning. Theoretical uncertainties in the neutrino
signal time profiles are estimated by applying the method to two widely
different supernova models. Present detectors can reach a sensitivity down to 1
eV. This is better than limits from tritium $\beta$-decay experiments,
competitive with the most conservative results from neutrinoless double
$\beta$-decay, less precise but less dependent from prior assumptions than
cosmological bounds. Future megaton water Cerencov detectors will allow for
about a factor of two improvement. However, they will not be competitive with
the next generation of laboratory experiments.
