The MP2/6-311++G(d,p) calculations were performed on several hydrogen-bonded systems. Different complexes were taken into account to analyze various types of hydrogen bonds, possessing different types of proton donors and proton acceptors as well as characterized by the broad range of the interaction energy. The Quantum Theory of Atoms in Molecules is applied. The results of the hybrid variational-perturbational approach are discussed. The unique properties of hydrogen bonds, where pi-electrons act as the proton acceptor (X-H center dot center dot center dot pi), are analyzed, and these interactions are compared with the other types of hydrogen bonds, mainly with C-H center dot center dot center dot Y interactions. It is shown that for X-H center dot center dot center dot pi systems the ellipticity at the bond critical point of the proton center dot center dot center dot acceptor interaction is much greater than for the other types of hydrogen bonds. However, both X-H center dot center dot center dot pi and C-H center dot center dot center dot Y interactions are characterized by the dominance of the dispersive energy.