We study quantum spin systems in the 1D, 2D square and 3D cubic lattices with nearest-neighbour XY-exchange. We use the coupled-cluster method (CCM) to calculate the ground-state energy, the T = 0 sublattice magnetization and the excited-state energies, all as functions of the anisotropy parameter . We consider the case with S = 1/2 in detail and give some results for higher S. In 1D these results are compared with the exact S = 1/2 results and in 2D with Monte Carlo and series expansions. We obtain critical points close to the expected value and our extrapolated LSUBn results for the ground-state energy are well converged for all except very close to the critical point.