The benzene dimer (BD) is an archetypal model of π∙∙∙π and C-H∙∙∙π noncovalent interactions as they occur in its cofacial and perpendicular arrangements, respectively. The enthalpic stabilization of the related BD structures has been debated for a long time and is revisited here. The revisit is based on results of computations that apply the coupled-cluster theory with singles, doubles and perturbative triples [CCSD(T)] together with large basis sets and extrapolate results to the complete basis set (CBS) limit in order to accurately characterize the three most important stationary points of the intermolecular interaction energy (ΔE) surface of the BD, which correspond to the tilted T-shaped (TT), fully symmetric T-shaped (FT) and slipped-parallel (SP) structures. In the optimal geometries obtained by searching extensive sets of the CCSD(T)/CBS ΔE data of the TT, FT and SP arrangements, the resulting ΔE values were -11.84, -11.34 and -11.21 kJ/mol, respectively. The intrinsic strength of the intermolecular bonding in these configurations was evaluated by analyzing the distance dependence of the CCSD(T)/CBS ΔE data over wide ranges of intermonomer separations. In this way, regions of the relative distances that favor BD structures with either π∙∙∙π or C-H∙∙∙π interactions were found and discussed in a broader context.