The constant-volume heat capacities, C-V, of various near-critical fluids with long-range potentials have been obtained using both canonical and grand-canonical Monte Carlo (GCMC) calculations. In the case of the restricted primitive model it is shown that the large discrepancies between previously reported results arise from the use of different simulation ensembles. In order to investigate how well the different ensemble estimates of C-V obtained with small systems can indicate the universality class of the bulk fluid, calculations have been performed for fluids with attractive pair interactions which vary like -1/r(a), with a=6, 4, and 3.1. For a=6, Ising-type criticality is expected, while for a=4 and 3.1 the criticality is mean-field. For each of these models the canonical-ensemble estimates of C-V do not provide unambiguous confirmation of the expected critical behavior, and hence this is not a reliable method for determining the universality class. This is also true of the GCMC estimates of C-V, which appear consistent with Ising-type behavior for all of the systems studied, even for those which are known to exhibit mean-field criticality in the thermodynamic limit. We suggest that these are artifacts associated with finite system size, and we speculate as to why they appear in canonical and GCMC calculations. (C) 2003 American Institute of Physics.