We perform extensive Monte Carlo simulations of binary hard-sphere mixtures (with diameter ratios of 5 and 10), to determine the entropic force between (1) a macrosphere and a hard wall, and (2) a pair of macrospheres. The microsphere background fluid (at volume fractions ranging from 0.1 to 0.34) induces an entropic force on the macrosphere(s); the latter component is at infinite dilution. We find good overall agreement, in both cases, with the predictions of a hypernetted chain-based theory for the entropic force. Our results also argue for the validity of the Derjaguin approximation relating the force between convex bodies to that between planar surfaces. The earlier Asakura-Oosawa theory, based on a simple geometric argument, is only accurate in the low-density limit.