Steady, inviscid, axisymmetric vortex flows past a sphere are obtained numerically as solutions of a partial differential equation for the stream function. The solutions found include vortex rings, bounded vortices attached to the sphere and infinite vortex tubes. Four families of attached vortices are described: vortex wakes behind the sphere, spherically annular vortices surrounding the spherical obstacle (which can be given analytically), bands of vorticity around the sphere and symmetric pairs of vortices fore and aft of the sphere. Each attached vortex leads to a one-parameter family of vortex rings, analogous to the connection between Hill's spherical vortex and the vortex rings of Norbury.