We show by cryogenic transmission electron microscopy that PbSe and CdSe nanocrystals of various shapes in a liquid colloidal dispersion self-assemble into equilibrium structures that have a pronounced dipolar character, to an extent that depends on particle concentration and size. Analyzing the cluster-size distributions with a one-dimensional (1D) aggregation model yields a dipolar pair attraction of 8-10 kBT at room temperature. This accounts for the long-range alignment of the crystal planes of individual nanocrystals in self-assembled superstructures and for anisotropic nanostructures grown via oriented attachment.