We have investigated the performance of a variety of density functional methods for weak intra- and intermolecular dispersion interactions. Grimme's empirical dispersion correction method is shown to give a good description for these interactions and helps to improve the description of water-hexamer isomers, noble-gas dimers, hydrocarbon C(12)H(12) isomers, branching energy of linear versus branched octane, dissociation of the covalently bound anthracene dimer, and stacking within the adenine dimer. However, the dispersion correction does not correct all shortcomings of the different density functionals, which leads to sizeable differences compared to ab initio CCSD(T) and experimental reference data. The only exception is shown to be our recently presented SSB-D functional that works well for all systems studied here.