  We consider four lepton-number violating (\lv) processes: (a) neutrinoless
double-beta decay (0\nu\beta\beta), (b) Delta L = 2 tau decays, (c) Delta L = 2
rare meson decays and (d) nuclear muon-positron conversion. In the absence of
exotic \lv interactions, the rates for these processes are determined by
effective neutrino masses <m>_{\ell_1\ell_2}, which can be related to the sum
of light neutrino masses, the neutrino mass-squared differences, the neutrino
mixing angles, a Dirac phase and two Majorana phases. We sample the
experimentally allowed ranges of <m>_{\ell_1\ell_2} based on neutrino
oscillation experiments as well as cosmological observations, and obtain a
stringent upper bound <m>_{\ell_1\ell_2} \lsim 0.14 eV. We then calculate the
allowed ranges for <m>_{\ell_1\ell_2} from the experimental rates of direct
searches for the above Delta L = 2 processes. Comparing our calculated rates
with the currently or soon available data, we find that only the
$0\nu\beta\beta$ experiment may be able to probe <m>_{ee} with a sensitivity
comparable to the current bound. Muon-positron conversion is next in
sensitivity, while the limits of direct searches for the other Delta L = 2
processes are several orders of magnitude weaker than the current bounds on
<m>_{\ell_1\ell_2}. Any positive signal in those direct searches would indicate
new contributions to the \lv interactions beyond those from three light
Majorana neutrinos.
