The applicability of various density functional theory (DFT) methods to describe the anisotropy of the intermolecular potential energy surfaces of hydrogen-bonded [OH--H2O, (H2O)(2)] and van der Waals [CO-H2O, He-CO2] complexes has been tested by comparison with supermolecule CCSD(T) (coupled-cluster method restricted to single, double, and noniterative triple excitations) and perturbational SAPT (symmetry-adapted perturbation theory) results computed for the same geometries and with the same basis sets. It is shown that for strongly bound ionic hydrogen-bonded complexes, like OH--H2O, hybrid approaches provide accurate results. For other systems, including the water dimer, the DFT calculations fail to reproduce the correct angular dependence of the potential surfaces. It is also shown that a hybrid functional adjusted to reproduce the CCSD(T) value of the binding energy for the water dimer produces results worse than the standard hybrid functionals for OH--H2O, and fails to describe the correct anisotropy of the CO-H2O interaction.