Shear viscosity of lipid membranes dictates how fast lipids, proteins, and other membrane constituents travel along the membrane and rotate around their principal axis, thus governing the rates of diffusion-limited reactions taking place at membranes. In this framework, the heterogeneity of biomembranes indicates that cells could regulate these rates via varying local viscosities. Unfortunately, experiments to probe membrane viscosity under various conditions are tedious and error prone. Molecular dynamics simulations provide an attractive alternative, especially given that recent theoretical developments enable the elimination of finite-size effects in simulations. Here, we use a variety of different equilibrium methods to extract the shear viscosities of lipid membranes from both coarse-grained and all-atom molecular dynamics simulations. We systematically probe the variables relevant for cellular membranes, namely, membrane protein crowding, cholesterol concentration, and the length and saturation level of lipid acyl chains, as well as temperature. Our results highlight that in their physiologically relevant ranges, protein concentration, cholesterol concentration, and temperature have significantly larger effects on membrane viscosity than lipid acyl chain length and unsaturation level. In particular, the crowding with proteins has a significant effect on the shear viscosity of lipid membranes and thus on the diffusion occurring in the membranes. Our work also provides the largest collection of membrane viscosity values from simulation to date, which can be used by the community to predict the diffusion coefficients or their trends via the Saffman-Delbrück description. Additionally, it is worth emphasizing that diffusion coefficients extracted from simulations exploiting periodic boundary conditions must be corrected for the finite-size effects prior to comparison with experiment, for which the present collection of viscosity values can readily be used. Finally, our thorough comparison to experiments suggests that there is room for improvement in the description of bilayer dynamics provided by the present force fields.