  Recently, the CoGeNT experiment has reported events in excess of expected
background. We analyze dark matter scenarios which can potentially explain this
signal. Under the standard case of spin independent scattering with equal
couplings to protons and neutrons, we find significant tensions with existing
constraints. Consistency with these limits is possible if a large fraction of
the putative signal events is coming from an additional source of experimental
background. In this case, dark matter recoils cannot be said to explain the
excess, but are consistent with it. We also investigate modifications to dark
matter scattering that can evade the null experiments. In particular, we
explore generalized spin independent couplings to protons and neutrons, spin
dependent couplings, momentum dependent scattering, and inelastic interactions.
We find that some of these generalizations can explain most of the CoGeNT
events without violation of other constraints. Generalized couplings with some
momentum dependence, allows further consistency with the DAMA modulation
signal, realizing a scenario where both CoGeNT and DAMA signals are coming from
dark matter. A model with dark matter interacting and annihilating into a new
light boson can realize most of the scenarios considered.
