Several groups have identified an extended excess of gamma rays over the modeled foreground and background emissions towards the Galactic center (GC) based on observations with the Fermi Large Area Telescope. This excess emission is compatible in morphology and spectrum with a telltale sign from dark matter (DM) annihilation. Here, we present a critical reassessment of DM interpretations of the GC signal in light of the foreground and background uncertainties that some of us recently outlaid in Calore et al. (2014). We find that a much larger number of DM models fits the gamma-ray data than previously noted. In particular: (1) In the case of DM annihilation into b¯b, we find that even large DM masses up to mχ≃74  GeV are allowed at p-value >0.05. (2) Surprisingly, annihilation into nonrelativistic hh gives a good fit to the data. (3) The inverse Compton emission from μ+μ- with mχ∼60–70  GeV can also account for the excess at higher latitudes, |b|>2°, both in its spectrum and morphology. We also present novel constraints on a large number of mixed annihilation channels, including cascade annihilation involving hidden sector mediators. Finally, we show that the current limits from dwarf spheroidal observations are not in tension with a DM interpretation when uncertainties on the DM halo profile are accounted for.