  We provide an argument based on flux insertion to show that certain
superconductors with a non-trivial topological invariant have protected zero
modes in their vortex cores. This argument has the flavor of a two dimensional
index theorem and applies to disordered systems as well. It also provides a new
way of understanding the zero modes in the vortex cores of a spinless $p_{x} +
i p_{y}$ superconductor. Applying this approach to superconductors with and
without time reversal and spin rotational symmetry, we predict the necessary
and sufficient conditions for protected zero modes to exist in their vortices.
