Weak interactions between organic donor and acceptor molecules resulting in cofacially-stacked aggregates ("CT complexes") were studied by second-order many-body perturbation theory (MP2) and by gradient-corrected hybrid Hartree-Fock/density functional theory (B3LYP exchange-correlation functional). The complexes consist of tetrathiafulvalene (TTF) and related compounds and tetracyanoethylene (TCNE). Density functional theory (DFT) and MP2 molecular equilibrium geometries of the component structures are calculated by means of 6-31G*, 6-31G*(0.25), 6-31++G**, 6-31++G(3df,2p) and 6-311G** basis sets. Reliable molecular geometries are obtained for the donor and acceptor compounds considered. The geometries of the compounds were kept frozen in optimizing aggregate structures with respect to the intermolecular distance. The basis set superposition error (BSSE) was considered (counterpoise correction). According to the DFT and MP2 calculations laterally-displaced stacks are more stable than vertical stacks. The charge transfer from the donor to the acceptor is small in the ground state of the isolated complexes. The cp-corrected binding energies of TTF/TCNE amount to -1.7 and -6.3 kcal/mol at the DFT(B3LYP) and MP2(frozen) level of theory, respectively (6-31G* basis set). Larger binding energies were obtained by Hobza's 6-31G*(0.25) basis set. The larger MP2 binding energies suggest that the dispersion energy is underestimated or not considered by the B3LYP functional. The energy increases when S in TTF/TCNE is replaced by O or NH but decreases with substitution by Se. The charge-transferred complexes in the triplet state are favored in the vertical arrangement. Self-consistent-reaction-field (SCRF) calculations predicted a gain in binding energy with solvation for the ground-state complex. The ground-state charge transfer between the components is increased up to 0.8 e in polar solvents.