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 $<sigma_A v >_{gammagamma}$ 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.
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