The 16th Neutrino Telescope Conference is underway.
One notable early result puts the sum of the three neutrino masses between the 0.056 eV lower bound from oscillation experiments, and an upper bound of 0.14 eV at a 95% confidence interval. This is almost, but not quite, tight enough to distinguish between a "normal" and an "inverted" neutrino mass hierarchy. This means that the absolute masses of the neutrinos are now known with a precision rivaling that of the up quark.
State of the art direct measurements of absolute neutrino masses which are in the process of being carried out would place only a 0.4 eV cap on the mass of the electron neutrino, which we know from cosmology must actually be less than about 0.05 eV, and in a normal hierarchy is likely to be about 0.001 eV or less.
UPDATED March 5, 2015:
The lastest neutrinoless double beta decay exclusion from GERDA at a 90% confidence interval is now a low limit on the half-life of neutrinoless double beta decay of 2.1*10^25 years. This is unchanged since last summer.