NMR spectroscopic parameters of the proton involved in hydrogen bonding are studied theoretically. The set of molecules includes systems with internal resonance-assisted hydrogen bonds, internal hydrogen bonds but no resonance stabilization, the acetic acid dimer (AAD), a DNA base pair, and the hydrogen succinate anion (HSA). Ethanol and guanine represent reference molecules without hydrogen bonding. The calculations are based on zero-point vibrationally averaged molecular structures in order to include anharmonicity effects in the NMR parameters. An analysis of the calculated NMR shielding and J-coupling is performed in terms of "chemist's orbitals", that is, localized molecular orbitals (LMOs) representing lone-pairs, atomic cores, and bonds. The LMO analysis associates some of the strong de-shielding of the protons in resonance-assisted hydrogen bonds with delocalization involving the π-backbone. Resonance is also shown to be an important factor causing de-shielding of the OH protons for AAD and HSA, but not for the DNA base pair. Nitromalonamide (NMA) and HSA have particularly strong hydrogen bonds exhibiting signs of covalency in the associated J-couplings. The analysis results show how NMR spectroscopic parameters that are characteristic for hydrogen bonded protons are influenced by the geometry and degree of covalency of the hydrogen bond as well as intra- and intermolecular resonance.