We present an analytical model to describe the stability of arbitrary semiconducting nanoparticle (NP) superlattices as a function of the dipole and polarizability of their constituents. We first validate our model by comparison with density functional theory calculations of simple cubic superlattices of small CdSe NPs, and we show the existence of a regime, relevant to experiments, where NP interactions are predominantly dipole-like. We then apply our model to binary superlattices and find striking differences between the stable geometries of lattices composed of polarizable and nonpolarizable NPs. Finally, we discuss the interplay of dipolar and ligand-ligand interactions in determining the stability of NP superlattices.