A detailed study of the single-particle dynamics of liquid water in normal and supercooled regime has been carried out by comparing molecular dynamics (MD) simulation results with now available high resolution quasielastic neutron scattering (PENS) data, Simulation runs have been performed at 264, 280, 292, and 305 K, using the extended simple point charge model, well suited for reproducing single-particle properties of H2O. The microscopic dynamics has been probed over a wide range of times and distances. The MD results indicate that a substantial coupling between translational and rotational dynamics exists already at about 1 ps. The decay of the translational dynamic correlations has been phenomenologically analyzed in terms of three exponential components, and the agreement between the parameters thus obtained from experimental and simulation derived datasets is quite satisfactory. Both QENS and MD data can not be described with sufficient accuracy by simple diffusion models over the entire range of examined wave vectors.