  We conduct a comprehensive search for X-ray emission lines from sterile
neutrino dark matter, motivated by recent claims of unidentified emission lines
in the stacked X-ray spectra of galaxy clusters and the centers of the Milky
Way and M31. Since the claimed emission lines lie around 3.5 keV, we focus on
galaxies and galaxy groups (masking the central regions), since these objects
emit very little radiation above $\sim 2$ keV and offer a clean background
against which to detect emission lines. We develop a formalism for maximizing
the signal-to-noise of decaying dark matter emission lines by weighing each
X-ray event according to the expected dark matter profile. In total, we examine
81 and 89 galaxies with Chandra and XMM-Newton respectively, totaling 15.0 and
14.6 Ms of integration time. We find no significant evidence of any emission
lines, placing strong constraints on the mixing angle of sterile neutrinos with
masses between 4.8-12.4 keV. In particular, if the 3.57 keV feature from Bulbul
et al. (2014) were due to 7.1 keV sterile neutrino emission, we would have
detected it at $4.4\sigma$ and $11.8\sigma$ in our two samples. The most
conservative estimates of the systematic uncertainties reduce these constraints
to $4.4\sigma$ and 7.8$\sigma$, or letting the line energy vary between 3.50
and 3.60 keV reduces these constraints to $2.7\sigma$ and $11.0\sigma$
respectively. Unlike previous constraints, our measurements do not depend on
the model of the X-ray background or on the assumed logarithmic slope of the
center of the dark matter profile.
