  Graphene has an unusual low-energy band structure with four chiral bands and
half-quantized and quantized Hall effects that have recently attracted
theoretical and experimental attention. We study the Fermi energy and disorder
dependence of its spin Hall conductivity. In the metallic regime we find that
vertex corrections enhance the intrinsic spin Hall conductivity and that skew
scattering can lead to its values that exceed the quantized ones expected when
the chemical potential is inside the spin-orbit induced energy gap. We predict
that large spin Hall conductivities will be observable in graphene even when
the spin-orbit gap does not survive disorder.
