Electric field gradients at the oxygen and hydrogen nuclei of water have been calculated using high level ab initio methods. Systematic studies of basis set truncation errors have been carried out at the Hartree-Fock and coupled cluster singles and doubles (CCSD) levels using extended correlation consistent basis sets with up to 398 basis functions. Correlation effects are investigated using a hierarchy of correlation methods extending up to the approximate inclusion of triples excitations by means of the CCSD(T) method. Rovibrational effects have been calculated combining accurate ab initio electric field gradient data and accurate experimental force fields. On the basis of the most accurate results for the electric field gradients, the nuclear quadrupole coupling constants for deuterium and oxygen-17 have been discussed including the temperature dependence. The final results are discussed in view of existing experimental data. Our best values for the nuclear quadrupole coupling constants are in excellent agreement (within 1%) of recent experimental results, while some earlier experimental values are shown to be less reliable.