In several papers (including a recent one by Banks and Seiberg) people mention a "folk-theorem" about the impossibility to have global symmetries in a consistent theory of quantum gravity. I remember having heard one particular argument that seemed quite reasonable (and almost obvious), but I can't remember it.
I have found other arguments in the literature, including (forgive my sloppiness):
In string theory global symmetries on the world-sheet become gauge symmetries in the target space, so there is no (known) way to have global symmetries.
in AdS/CFT global symmetries on the boundary correspond to gauge symmetries in the bulk so there again there is no way to have global symmetries in the bulk.
The argument in the Banks-Seiberg paper about the formation of a black hole charged under the global symmetry.
I find none of these completely satisfactory. Does anybody know of better arguments?