The convergence behavior of the total and correlation energies of He, H-2, and He-2 with the increase of basis quality in the correlation-consistent basis sets, cc-pVXZ and aug-cc-pVXZ(X = D,T,Q,5,6), was studied to search for a proper extrapolation scheme to predict the accurate complete basis set (CBS) limits at the MP2, CCSD, and CCSD(T) level. The functional form employed for extrapolation is a simple polynomial including inverse cubic power and higher-order terms of the cardinal number X in the correlation-consistent basis set as well as exponential function. It is found that a simple extrapolation of two successive correlation-consistent basis set energies (total or correlation energies) using (X + k)(-3) [k = 0 for MP2 and k = -1 for CCSD and CCSD(T) level] gives in general the most reliable (and accurate in case of total energy) estimates to the CBS limit energies. It is also shown that the choice of proper basis set, which can represent the electronic motions in the fragment and complex equally well, appears necessary for reliable estimate of the relative energies such as the binding energy of the complex. From the extrapolation of aug-cc-pV5Z and aug-cc-pV6Z energies with (X + k)(-3), we obtained 21.3(21.4), 28.4(29.0) and 33.2(33.8) microhartrees as the CBS limit binding energy of He-2 at the internuclear separation of 5.6 a.u. at the MP2, CCSD, and CCSD(T) level, respectively, with the values in parentheses representing the exact CBS limit binding energies.