  It is well known that spinors on oriented Riemannian manifolds cannot be
defined as sections of a vector bundle associated with the frame bundle. For
this reason spin and spin^c structures are often introduced. In this paper we
prove that spin^c structures have a universal property among all other
structures that enable the construction of spinor bundles. We proceed to prove
a similar result for metaplectic^c structures on symplectic manifolds.
