  Dark matter detectors built primarily to probe elastic scattering of WIMPs on
nuclei are also precise probes of light, weakly coupled particles that may be
absorbed by the detector material. In this paper, we derive constraints on the
minimal model of dark matter comprised of long-lived vector states V (dark
photons) in the 0.01-100 keV mass range. The absence of an ionization signal in
direct detection experiments such as XENON10 and XENON100 places a very strong
constraint on the dark photon mixing angle, down to $O(10^{-15})$, assuming
that dark photons comprise the dominant fraction of dark matter. This
sensitivity to dark photon dark matter exceeds the indirect bounds derived from
stellar energy loss considerations over a significant fraction of the available
mass range. We also revisit indirect constraints from $V\to 3\gamma$ decay and
show that limits from modifications to the cosmological ionization history are
comparable to the updated limits from the diffuse gamma-ray flux.
