Neutral and charged assemblies of π-conjugated molecules span the field of organic electronics. Electronic structure computations can provide valuable information regarding the nature of the intermolecular interactions within molecular precursors to organic electronics. Here, we introduce a database of neutral (Pi29n) and radical (Orel26rad) dimer complexes that represent binding energies between organic functional units. The new benchmarks are used to test approximate electronic structure methods. Achieving accurate interaction energies for neutral complexes (Pi29n) is straightforward, so long as dispersion interactions are properly taken into account. However, π-dimer radical cations (Orel26rad) are examples of highly challenging situations for density functional approximations. The role of dispersion corrections is crucial, yet simultaneously long-range corrected exchange schemes are necessary to provide the proper dimer dissociation behavior. Nevertheless, long-range corrected functionals seriously underestimate the binding energy of Orel26rad at equilibrium geometries. In fact, only ωB97X-D, an empirical exchange-correlation functional fitted together with an empirical “classical” dispersion correction, leads to suitable results. Valuable alternatives are the more demanding MP2/6-31G*(0.25) level, as well as the most cost-effective combination involving a dispersion corrected long-range functional together with a smaller practical size basis set (e.g., LC-ωPBEB95-dDsC/6-31G*). The Orel26rad test set should serve as an ideal benchmark for assessing the performance of improved schemes.