Ab initio results are presented for the low-lying bound states of O2 that dissociate to ground-state atoms. Spectroscopic constants and dissociation energies (D(e)) are reported for the X 3-SIGMA-g-, a 1-DELTA-g, b 1-SIGMA-g+, c 1-SIGMA-u-, A' 3-DELTA-u, A 3-SIGMA-u+, 3-PI-u, 5-SIGMA-u-, 5-PI-u, and 5-PI-g states. For the first six states, which have been experimentally characterized, we obtain accurate results at the multireference configuration-interaction level after correction for higher excitations. For example, our computed D(e) value for the X 3-SIGMA-g- state corrected for basis-set superposition error is only 0.7 kcal/mol less than the experimental value. The 5-PI-g state is estimated to have a D(e) of 0.16 +/- 0.03 eV, suggesting that the importance of this state in the nightglow should perhaps be reconsidered.