The Newtonian shear viscosity, eta(S), of near-hard-sphere colloidal particle liquids from many sources at various packing fractions is compared with that of the pure hard sphere fluid which can be calculated essentially exactly by molecular dynamics, MD, computer simulations. The experimental relative viscosities for the colloidal systems, eta(S) / eta(0) , where eta(0) is the viscosity of the solvent, generally lie in between two curves formed from the hard-sphere data, namely, eta(S) / eta(B) as an upper bound and the inverse self-diffusion coefficient, D-B /D, as the lower bound, where eta(B) and D-B are the Boltzmann transport coefficients accurate at low densities. Brownian dynamics simulation values of eta(S) / eta(0) and D-0 / D-L where D-L is the long-time self-diffusion coefficient are close to this lower bound which indicates that Brownian motion alone without hydrodynamic interactions underestimates the viscosity of the system. Hydrodynamic effects increase the viscosity closer to the pure hard-sphere curve obtained by MD. The ratio, D-0 / D-L obtained from the experimental data increases slightly more rapidly than eta(S) / eta(L) at high packing fractions. There is a near-linear relationship between the inverse viscosity (fluidity) and self-diffusion coefficient with inverse packing fraction for the hard-sphere fluid, the former proposed by Dymond (1974). This analytic form accounts reasonably well for the corresponding quantities of the colloidal systems as well. We analyzed the values of the relative viscosities at 50% packing fraction. We conclude that the value is similar to 40 for the pure hard sphere fluid itself from recent molecular dynamics simulations by of Sigurgeirsson and Heyes (2003), and probably similar to 25+/-5 from experiments on real near-hard sphere colloids (although the experimental scatter is quite large), and similar to 10 by Brownian dynamics computer simulations. For the long time self-diffusion coefficient the ratio is similar to 40+/-10 for experimental colloidal systems, and similar to 10 from simulation by molecular dynamics and Brownian dynamics. The infinite frequency shear viscosity has a ratio similar to 10 and the short-time self-diffusion coefficient ratio is similar to 4, both of which are somewhat lower than their long-time counterparts. The shear viscosity at finite shear rates in the second Newtonian plateau typically lies in between the values of the Newtonian viscosity and the infinite frequency viscosity (i.e., similar to 15+/-5). (C) 2004 The Society of Rheology.