  In a broad class of consistent models, MeV to few-GeV dark matter interacts
with ordinary matter through weakly coupled GeV-scale mediators. We show that a
suitable meter-scale (or smaller) detector situated downstream of an electron
beam-dump can sensitively probe dark matter interacting via sub-GeV mediators,
while B-factory searches cover the 1-5 GeV range. Combined, such experiments
explore a well-motivated and otherwise inaccessible region of dark matter
parameter space with sensitivity several orders of magnitude beyond existing
direct detection constraints. These experiments would also probe invisibly
decaying new gauge bosons ("dark photons") down to kinetic mixing of \epsilon ~
10^{-4}, including the range of parameters relevant for explaining the
(g-2)_{\mu} discrepancy. Sensitivity to other long-lived dark sector states and
to new milli-charge particles would also be improved.
