We investigate the effects of zero-point vibrational motion on the nuclear magnetic shielding constants of a large number of organic molecules. The vibrational corrections include anharmonic contributions from the potential energy surface and harmonic contributions from the curvature of the property surface. Particular attention is paid to vibrational corrections to hydrogen shielding constants where we show that vibrational corrections may be substantial, ranging from about +0.50 to -0.70 ppm, and thus demonstrating that ignoring these effects may give errors in the chemical shifts by more than 1 ppm in certain extreme cases. These effects can therefore not be neglected when comparing calculated results with experiment, not even for the chemical shifts. However, we also demonstrate that the vibrational corrections to the hydrogen shieldings are to a large extent transferable from one molecule to another. We have tabulated functional vibrational corrections to the hydrogen shieldings, based on results for more than 35 molecules. Unfortunately, no similar transferability has been observed for the vibrational corrections to shielding constants of other nuclei such as carbon, nitrogen, or oxygen.