  We present a classification of SU(3) x SU(2) x U(1) gauge invariant \Delta L
= 2 (L being lepton number) effective operators relevant for generating small
Majorana neutrino masses. Operators of dimension up to 11 have been included in
our analysis. This approach enables us to systematically identify interesting
neutrino mass models. It is shown that many of the well-known models fall into
this classification. In addition, a number of new models are proposed and their
neutrino phenomenology is outlined. Of particular interest is a large class of
models in which neutrinoless double beta decays arise at a lower order compared
to the neutrino mass, making these decays accessible to the current round of
experiments.
