Using mixed-field finite-size scaling simulations, we have investigated the liquid-vapor critical behavior of three-dimensional fluids;vith algebraically decaying attractive pair interactions, which vary like -1/r(3+sigma) with sigma = 3, 1, and 0.1. The finite-size scaling analysis was carried out by matching the critical ordering operator distribution, p(L)(x), against the limiting Ising form, i.e., Ising criticality was assumed. When the potential is short-ranged (sigma = 3) the simulation results are entirely consistent with the expected Ising critical behavior. When the potential is long-ranged (sigma = 1, 0.1), however, marked deviations from Ising behavior are observed, particularly in the form of the critical ordering operator distribution, and in the estimated values of beta/nu. The results are consistent with non-Ising criticality which is predicted theoretically in fluid with long-range interactions. Some results from Gibbs ensemble simulations are also provided in order to sketch the shape of the liquid-vapor coexistence envelope. We discuss the relevance of our results to the current issue of criticality in ionic fluids.