  Can dark matter be stabilized by charge conservation, just as the electron is
in the standard model? We examine the possibility that dark matter is hidden,
that is, neutral under all standard model gauge interactions, but charged under
an exact U(1) gauge symmetry of the hidden sector. Such candidates are
predicted in WIMPless models, supersymmetric models in which hidden dark matter
has the desired thermal relic density for a wide range of masses. Hidden
charged dark matter has many novel properties not shared by neutral dark
matter: (1) bound state formation and Sommerfeld-enhanced annihilation after
chemical freeze out may reduce its relic density, (2) similar effects greatly
enhance dark matter annihilation in protohalos at redshifts of z ~ 30, (3)
Compton scattering off hidden photons delays kinetic decoupling, suppressing
small scale structure, and (4) Rutherford scattering makes such dark matter
self-interacting and collisional, potentially impacting properties of the
Bullet Cluster and the observed morphology of galactic halos. We analyze all of
these effects in a WIMPless model in which the hidden sector is a simplified
version of the minimal supersymmetric standard model and the dark matter is a
hidden sector stau. We find that charged hidden dark matter is viable and
consistent with the correct relic density for reasonable model parameters and
dark matter masses in the range 1 GeV < m_X < 10 TeV. At the same time, in the
preferred range of parameters, this model predicts cores in the dark matter
halos of small galaxies and other halo properties that may be within the reach
of future observations. These models therefore provide a viable and
well-motivated framework for collisional dark matter with Sommerfeld
enhancement, with novel implications for astrophysics and dark matter searches.
