The radiative effect of well-mixed greenhouse gases (WMGHGs) is probably the most significant anthropogenic forcing of the climate system. The most comprehensive tools for simulating past and future climates influenced by WMGHGs are fully coupled atmosphere-ocean general circulation models (GCMs). Because of the importance of WMGHGs as forcing agents, it is essential that GCMs compute the radiative forcing by these gases as accurately as possible. We present the results of an intercomparison between the forcings computed by GCMs and by benchmark line-by-line (LBL) radiative transfer codes. The comparison is focused on forcing by CO2, CH4, N2O, CFC-11, CFC-12, and the increased H2O expected in warmer climates. The models participating in the intercomparison include representatives from many of the modeling groups participating in the IPCC 4th Assessment Report (AR4) and from a number of the principal groups developing LBL codes. The results indicate that there are still substantial discrepancies between GCMs and LBL models for forcings by CH4, N2O, and CO2. We quantify these differences and discuss the implications for interpreting variations in forcing and response across the multi-model ensemble of GCM simulations assembled for the IPCC AR4.