Computer simulations using density functional theory based ab initio path integral molecular dynamics have been carried out to investigate hydrogen bonding in water under ambient conditions. Structural predictions for both H2O and D2O, which include the effects of zero-point energy, thermal motion, and many body polarization effects, are contrasted with classical simulations that ignore nuclear quantum effects. The calculated effect of H/D isotope substitution on the water structure is much smaller than the difference between the classical and quantum path integral results, and is in excellent agreement with the measured H/D difference data from both neutron and x-ray scattering.