Range-separated methods combining a short-range density functional with long-range random phase approximations (RPA) with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurečka,Šponer,Černý, and Hobza (Phys. Chem. Chem. Phys. 8, 1985Phys. 8, , 2006. The methods are also compared to full-range RPA approaches. Both range separation and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermolecular interaction energies. The best results are obtained with the method called RSH+RPAx which yields interaction energies for the S22 set with an estimated mean absolute error of about 0.5 -0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7 -9%, depending on the reference interaction energies used. In particular, the RSH+RPAx method is found to be overall more accurate than the range-separated method based on long-range second-order Møller-Plesset (MP2) perturbation theory (RSH+MP2).