  Dark-matter annihilation into electroweak gauge and Higgs bosons results in
$\gamma$-ray emission. We use observational upper limits on the fluxes of both
line and continuum $\gamma$-rays from the Milky Way Galactic Center and from
Milky Way dwarf companion galaxies to set exclusion limits on allowed
dark-matter masses. (Generally, Galactic Center $\gamma$-ray line search limits
from the Fermi-LAT and the H.E.S.S. experiments are most restrictive.) Our
limits apply under the following assumptions: a) the dark matter species is a
cold thermal relic with present mass density equal to the measured dark-matter
density of the universe; b) dark-matter annihilation to standard-model
particles is described in the non-relativistic limit by a single effective
operator ${\cal O} \propto J_{DM}\cdot J_{SM}$, where $J_{DM}$ is a
standard-model singlet current consisting of dark-matter fields (Dirac fermions
or complex scalars), and $J_{SM}$ is a standard-model singlet current
consisting of electroweak gauge and Higgs bosons; and c) the dark-matter mass
is in the range 5 GeV to 20 TeV. We consider, in turn, the 34 possible
operators with mass dimension 8 or lower with non-zero s-wave annihilation
channels satisfying the above assumptions. Our limits are presented in a large
number of figures, one for each of the 34 possible operators; these limits can
be grouped into 13 classes determined by the field content and structure of the
operators. We also identify three classes of operators (coupling to the Higgs
and $SU(2)_L$ gauge bosons) that can supply a 130 GeV line with the desired
strength to fit the putative line signal in Fermi data, while saturating the
relic density and satisfying all other indirect constraints we consider.
