  General considerations in general relativity and quantum mechanics are known
to potentially rule out continuous global symmetries in the context of any
consistent theory of quantum gravity. Assuming the validity of such
considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray,
neutrino, and CMB data on models that invoke global symmetries to stabilize the
dark matter particle. We compute up-to-date, robust model-independent limits on
the dark matter lifetime for a variety of Planck-scale suppressed
dimension-five effective operators. We then specialize our analysis and apply
our bounds to specific models including the Two-Higgs-Doublet, Left-Right,
Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. {Assuming that
(i) global symmetries are broken at the Planck scale, that (ii) the
non-renormalizable operators mediating dark matter decay have $O(1)$ couplings,
that (iii) the dark matter is a singlet field, and that (iv) the dark matter
density distribution is well described by a NFW profile}, we are able to rule
out fermionic, vector, and scalar dark matter candidates across a broad mass
range (keV-TeV), including the WIMP regime.
