The role of dipole-dipole interactions in the self-assembly of dipolar organic molecules on surfaces is investigated. As a model system, strongly dipolar model molecules, p-benzoquinonemonoimine zwitterions (ZI) of type C6H2(⋯ NHR)2(⋯ O)2 on crystalline coinage metal surfaces were investigated with scanning tunneling microscopy and first principles calculations. Depending on the substrate, the molecules assemble into small clusters, nano gratings, and stripes, as well as in two-dimensional islands. The alignment of the molecular dipoles in those assemblies only rarely assumes the lowest electrostatic energy configuration. Based on calculations of the electrostatic energy for various experimentally observed molecular arrangements and under consideration of computed dipole moments of adsorbed molecules, the electrostatic energy minimization is ruled out as the driving force in the self-assembly. The structures observed are mainly the result of a competition between chemical interactions and substrate effects. The substrate’s role in the self-assembly is to (i) reduce and realign the molecular dipole through charge donation and back donation involving both the molecular HOMO and LUMO, (ii) dictate the epitaxial orientation of the adsorbates, specifically so on Cu(111), and (iii) inhibit attractive forces between neighboring chains in the system ZI/Cu(111), which results in regularly spaced molecular gratings.