We calculate the rovibrational corrections, temperature dependence and isotope shifts of the isotropic and anisotropic nuclear shieldings of the water molecule. This is the first correlated study of rovibrational effects on the nuclear shieldings in the water molecule and the first study of these effects on the shielding anisotropies. The use of a large restricted active space self-consistent field wave function and a large basis set ensures that the results are of high accuracy. The rovibrational corrections are found to be substantial, 3.7% and 1.8% for the isotropic oxygen and hydrogen shieldings, respectively, in the (H2O)-H-1-O-17 isotopomer at 300 K. For the shielding anisotropies and asymmetry parameters, the corresponding relative corrections are even larger. The changes in the shielding tensors due to molecular rotation and vibration are of the same order of magnitude as-and in some cases even exceed-the changes due to electron correlation. The accuracy of our calculated rovibrationally corrected oxygen shielding leads us to propose a new absolute shielding scale for the O-17 nucleus : 324.0 +/-1.5 ppm for the O-17 shielding of (H2O)-H-1-O-17 in the gas phase (300 K). This shielding scale is supported by recent high-level CCSD(T) calculations on carbon monoxide. The absolute oxygen shielding constants of some oxygen-containing molecules are calculated using the new shielding scale and experimental data on oxygen chemical shifts, comparing the absolute shieldings to the results of recent high-level theoretical calculations.