The accuracy of atomization energies obtained from explicitly correlated coupled-cluster R12 calculations (CC-R12)-including single and double excitation operators (CCSD-R12) and a posteriori perturbative corrections for triple excitations [CCSD[T]-R12 and CCSD(T)-R12]-is studied for CH2((1)A(1)), NH3, H2O, HF, N-2, CO, and F-2. The basis-set convergence with functions of high angular momentum is demonstrated. Unlike for conventional calculations, already the spdf saturation on nonhydrogen atoms and spd saturation on hydrogen are sufficient for CC-R12 calculations to provide results accurate to within 1 kJ/mol of the limit of a complete basis. Remaining small uncertainties at the CCSD[T]-R12 or CCSD(T)-R12 levels are attributed to the insufficient convergence within the coupled-cluster hierarchy towards the limit of full configuration interaction. It is shown that near the basis-set limit (as provided by CC-R12 calculations) the CCSD[T] variant of the triples correction gives, on average, results closer to the experimental data than its CCSD(T) counterpart. Approximate error bars are estimated by one single CC-R12 calculation from the difference between the CCSD[T] and CCSD(T) methods and from the second-order electronic cusp correction in standard approximation B.