Nanoparticles often self-assemble into hexagonal-close-packed (hcp) structures although it is predicted to be less stable than face-centered-cubic (fcc) packing in hard-sphere models. In addition to close-packed fcc and hcp superlattices, we observe formation of nonclose-packed simple-hexagonal (sh) superlattices of nearly spherical PbS, PbSe, and gamma-Fe2O3 nanocrystals. This surprisingly rich phase diagram of monodisperse semiconducting nanoparticles is explained by considering the interactions between nonlocal dipoles of individual nanoparticles. By calculating the total electrostatic and dispersive energies, we explain stability of the hcp and sh nanoparticle superlattices, introduce the superlattice phase diagram, and predict antiferroelectric ordering in dipolar nanoparticle superlattices.