The non-Newtonian behavior of dilute polymer solutions is investigated by computer simulation of a bead-and-spring model, using the Brownian dynamics technique to evaluate the shear rate dependence of the intrinsic viscosity. This behavior is a consequence of the combined effects of hydrodynamic interaction, excluded volume, and finite extensibility. The simulations allow the study of the influence of each effect separately. When all the effects are considered, the simulation results can be compared to experimental data of solution viscosities, which are available just in the region of moderately small shear rates. Data from molecular architecture and other solution properties are obtained to parametrize the bead-and-spring model, with emphasis in the description of the chain extensibility. Comparison of simulation and experimental results is presented for both highly flexible vinyl polymers and locally stiff cellulose chains.