The porosity dependence of Poisson's ratio of materials with random microstructure is investigated via analytical and numerical modeling. It is shown that all analytical models predict porosity independence if the solid Poisson ratio is 0.2 and for low porosities a converging trend toward this value with increasing porosity. From all theory-based relations, only power-law and exponential relations allow for auxetic behavior. Numerical calculations on computer-generated digital microstructures (overlapping and isolated spherical pores, pores between overlapping spherical grains, wall-based cellular materials/closed-cell foams, and strut-based cellular materials/open-cell foams) confirm the general qualitative trends of the analytical models, although a closer look reveals significant quantitative differences. Cellular materials and foams exhibit similar features as porous materials in general, but lack their converging trend toward values around 0.2. Comparison of our results with the classical Roberts-Garboczi results shows good agreement, with subtle differences due to the different microstructures generated.