Continuous-energy Monte Carlo eigenvalue calculations have been performed for a selection of HEU-MET-FAST, IEU-MET-FAST, HEU-SOL-THERM, LEU-COMP-THERM, and LEU-SOL-THERM benchmarks using ENDF/B (primarily VI.8), JEFF-3.0, and JENDL-3.3 cross sections. These benchmarks allow for testing the cross-section data for both common reactor nuclides such as 1H, 16O, and 235,238U and structural and shielding elements such as Al, Ti, Fe, Ni, and Pb. The latest cross-section libraries yield near-unity eigenvalues for unreflected or water-reflected HEU-SOL-THERM and LEU-SOL-THERM systems. Near-unity eigenvalues are also obtained for bare HEU-MET-FAST and IEU-MET-FAST systems, but small deviations from unity are observed in both FAST and THERM benchmarks as a function of nonhydrogenous reflector material and thickness. The long-standing problem of lower eigenvalues in water-reflected low-enriched-uranium fuel lattice systems remains, regardless of cross-section library.