Although density functional theory (DFT) is more and more commonly used as a very efficient tool for the study of molecules and bulk materials, its applications to weakly bonded systems remain rather sparse in the literature, except studies that consider hydrogen bonding. It is, however, of essential interest to be able to correctly describe weaker van der Waals complexes. This prompted us to investigate more precisely the reliability of several widely-used functionals. The equilibrium geometries and the binding energies of C6H6···X (X = O2, N2, or CO) complexes are determined within the standard Kohn−Sham approach of DFT using different exchange−correlation functionals and at the MP2 level of theory for comparison. It is comprehensively concluded that extreme care must be taken in the choice of the functional since only those that behave properly at large and intermediate values of the reduced density gradient s give relevant results. The PW91 exchange functional, the enhancement factor of which does not diverge at increasing s, appears as the most reliable for the studied systems. It is furthermore demonstrated that the quality of the DFT results is determined by the exchange energy component of the total energy functional.