  We study the gauged U(1)_{B-L} extensions of the models for neutrino masses
and dark matter. In this class of models, tiny neutrino masses are radiatively
induced through the loop diagrams, while the origin of the dark matter
stability is guaranteed by the remnant of the gauge symmetry. Depending on how
the lepton number is violated in the neutrino mass diagrams, these models are
systematically classified. We present a complete list for the one-loop Z_2 and
the two-loop Z_3 neutrino mass models as examples of the classification. These
underlying gauge symmetries and its breaking patterns can be probed at future
high energy colliders by looking at the width of the new gauge boson.
