In this work, the shear viscosity at ambient conditions of several water models (SPC/E, TIP4P, TIP5P, and TIP4P/2005) is evaluated using the Green-Kubo formalism. The performance of TIP4P/2005 is excellent, that of SPC/E and TIP5P is more or less acceptable, whereas TIP4P and especially TIP3P give a poor agreement with experiment. Further calculations have been carried out for TIP4P/2005 to provide a wider assessment of its performance. In accordance with experimental data, TIP4P/2005 predicts a minimum in the shear viscosity for the 273 K isotherm, a shift in the minimum toward lower pressures at 298 K, and its disappearance at 373 K.