  We study Ising systems of spins with dipolar interactions. We find a simple
approximate relation for the interaction energy between pairs of parallel
lattice columns of spins running along the Ising spin direction. This relation
provides insight into the relation between lattice geometry and the nature of
the ordered state. It can be used to calculate ground state energies. We have
also obtained ground state energies and ordering temperatures T_0 from Monte
Carlo simulations. Simple empirical relations, that give T_0 for simple and
body centered tetragonal lattices in terms of lattice parameters are also
established. Finally, the nature of the ordered state and T_0 are determined
for Fe_8 clusters, which crystallize on a triclinic lattice.
