In a previous paper, we have shown that counterions condense on charged spheres and planes as well as on the linear polyelectrolyte models of charged lines and cylinders, provided that the surface charge densities exceed a critical value. Here we give a more complete calculation resulting in the electrostatic free energies of all of these geometric shapes. We consider a macroion immersed in salt solution and also a macroion in the presence only of its own counterions. For a sphere, cylinder, and plane with equal surface charge densities, the sphere has the lowest electrostatic free energy and the plane the highest. We apply the results to the coil-to-globule transition and to the growth of spheres by fusion of two smaller spheres to form a larger one.