A recent study by Ahmed, Peterka, and Suits [J. Chem. Phys. 110, 4248 (1999)] has presented the first experimentally derived estimate of the singlet-triplet gap in the simplest alkyne, acetylene. Their value, T0 (a 3B2) = 28 900 cm-1, does not agree with previous theoretical predictions using the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] method and a triple-zeta plus double polarization plus f-function basis set (TZ2Pf), which yields 30 500 +/- 1000 cm-1. This discrepancy has prompted us to investigate possible deficiencies in this usually-accurate theoretical approach. Employing extrapolations to the complete basis set limit along with corrections for full connected triple excitations, core correlation, and even relativistic effects, we obtain a value of 30 900 cm-1 (estimated uncertainty +/- 230 cm-1), demonstrating that the experimental value is underestimated. To assist in the interpretation of anticipated future experiments, we also present highly accurate excitation energies for the other three low-lying triplet states of acetylene, a 3Bu (33 570 +/- 230 cm-1), b 3Au (36 040 +/- 260 cm-1), and b 3A2 (38 380 +/- 260 cm-1), and the three lowest-lying states of vinylidene, X 1A1 (15 150 +/- 230 cm-1), a 3B2 (31 870 +/- 230 cm-1) and b 3A2 (36 840 +/- 350 cm-1). Finally, we assess the ability of density functional theory (DFT) and the Gaussian-3 method to match our benchmark results for adiabatic excitation energies of C2H2.