  We study phenomenological implications of the ATLAS and CMS hint of a $125\pm
1$ GeV Higgs boson for the singlet, and singlet plus doublet non-supersymmetric
dark matter models, and for the phenomenology of the CMSSM. We show that in
scalar dark matter models the vacuum stability bound on Higgs boson mass is
lower than in the standard model and the 125 GeV Higgs boson is consistent with
the models being valid up the GUT or Planck scale. We perform a detailed study
of the full CMSSM parameter space keeping the Higgs boson mass fixed to $125\pm
1$ GeV, and study in detail the freeze-out processes that imply the observed
amount of dark matter. After imposing all phenomenological constraints except
for the muon $(g-2)_\mu,$ we show that the CMSSM parameter space is divided
into well separated regions with distinctive but in general heavy sparticle
mass spectra. Imposing the $(g-2)_\mu$ constraint introduces severe tension
between the high SUSY scale and the experimental measurements -- only the
slepton co-annihilation region survives with potentially testable sparticle
masses at the LHC. In the latter case the spin-independent DM-nucleon
scattering cross section is predicted to be below detectable limit at the
XENON100 but might be of measurable magnitude in the general case of light dark
matter with large bino-higgsino mixing and unobservably large scalar masses.
