  Dark matter annihilation into charged particles is necessarily accompanied by
gamma rays, produced via radiative corrections. Internal bremsstrahlung from
the final state particles can produce hard gamma rays up to the dark matter
mass, with an approximately model-independent spectrum. Focusing on
annihilation into electrons, we compute robust upper bounds on the dark matter
self annihilation cross section $<\sigma_A v >_{e^+e^-}$ using gamma ray data
from the Milky Way spanning a wide range of energies, $\sim10^{-3} - 10^4$ GeV.
We also compute corresponding bounds for the other charged leptons. We make
conservative assumptions about the astrophysical inputs, and demonstrate how
our derived bounds would be strengthened if stronger assumptions about these
inputs are adopted. The fraction of hard gamma rays near the endpoint
accompanying annihilation to $e^+e^-$ is only a factor of $\alt 10^2$ lower
than for annihilation directly to monoenergetic gamma rays. The bound on
$<\sigma_A v >_{e^+e^-}$ is thus weaker than that for $<\sigma_A v
>_{\gamma\gamma}$ by this same factor. The upper bounds on the annihilation
cross sections to charged leptons are compared with an upper bound on the {\it
total} annihilation cross section defined by neutrinos.
