The dissociation energy of molecular hydrogen is determined theoretically with a careful estimation of error bars by including nonadiabatic, relativistic, and quantum electrodynamics (QED) corrections. The relativistic and QED corrections were obtained at the adiabatic level of theory by including all contributions of the order α(2) and α(3) as well as the major (one-loop) α(4) term, where α is the fine-structure constant. The computed α(0), α(2), α(3), and α(4) components of the dissociation energy of the H2 isotopomer are 36 118.7978(2), -0.5319(3), -0.1948(2), and -0.0016(8) cm(-1), respectively, while their sum amounts to 36 118.0695(10) cm(-1), where the total uncertainty includes the estimated size (±0.0004 cm(-1)) of the neglected relativistic nonadiabatic/recoil corrections. The obtained theoretical value of the dissociation energy is in excellent agreement with the most recent experimental determination 36 118.0696(4) cm(-1) [J. Liu et al. J. Chem. Phys. 2009, 130, 174 306]. This agreement would have been impossible without inclusion of several subtle QED contributions which have not been considered, thus far, for molecules. A similarly good agreement is observed for the leading vibrational and rotational energy differences. For the D2 molecule we observe, however, a small disagreement between our value 36 748.3633(9) cm(-1) and the experimental result 36 748.343(10) cm(-1) obtained in a somewhat older and less precise experiment [Y. P. Zhang et al. Phys. Rev. Lett. 2004, 92, 203003]. The reason of this discrepancy is not known.