We explore, mostly using data from solar neutrino experiments, the hypothesis that the neutrino mass eigenstates are unstable. We find that, by combining $^8$B solar neutrino data with those on $^7$Be and lower-energy solar neutrinos, one obtains a mostly model-independent bound on both the $ u_1$ and $ u_2$ lifetimes. We comment on whether a nonzero neutrino decay width can improve the compatibility of the solar neutrino data with the massive neutrino hypothesis.