Second-order Moller-Plesset perturbation theory (MP2) is the most expedient wave function-based method for considering electron correlation in quantum chemical calculations and, as such, provides a cost-effective framework to assess the effects of basis sets on correlation energies, for which the complete basis set (CBS) limit can commonly only be obtained via extrapolation techniques. Software packages providing MP2 energies are commonly based on atom-centered bases with innate issues related to possible basis set superposition errors (BSSE), especially in the case of weakly bonded systems. Here, we present noncovalent interaction energies in the CBS limit, free of BSSE, for 20 dimer systems of the S22 data set obtained via a highly parallelized MP2 implementation in the plane-wave pseudopotential molecular dynamics package CPMD. The specificities related to plane waves for accurate and efficient calculations of gas-phase energies are discussed, and results are compared to the localized (aug-)cc-pV[D,T,Q,5]Z correlation-consistent bases as well as their extrapolated CBS estimates. We find that the BSSE-corrected aug-cc-pV5Z basis can provide MP2 energies highly consistent with the CBS plane wave values with a minimum mean absolute deviation of similar to 0.05 kcal/mol without the application of any extrapolation scheme. In addition, we tested the performance of 13 different extrapolation schemes and found that the X-3 expression applied to the (aug-)cc-pVXZ bases provides the smallest deviations against CBS plane wave values if the extrapolation sequence is composed of points D and T, while (X + 1/2)(-4) performs slightly better for TQ and Q5 extrapolations. Also, we propose A(X - 1/2)(-3) + B(X + 1/2)(-4) as a reliable alternative to extrapolate total energies from the DTQ, TQ5, or DTQ5 data points. In spite of the general good agreement between the values obtained from the two types of basis sets, it is noticed that differences between plane waves and (aug-)cc-pVXZ basis sets, extrapolated or not, tend to increase with the number of electrons, thus raising the question of whether these discrepancies could indeed limit the attainable accuracy for localized bases in the limit of large systems.