Hydrogen bond dynamics at the neat interface between water and a series of organic liquids are studied with molecular dynamics computer simulation. The organic liquids are nonpolar (carbon tetrachloride), weakly polar (1,2-dichloroethane), and polar (nitrobenzene). The effect of surface polarity and surface roughness is examined. The dynamics are expressed in terms of the hydrogen bond population autocorrelation functions and are found to be nonexponential and strongly dependent on the nature of the organic phase. In particular, at all interfaces, the dynamics are slower at the interface than in the bulk and sensitive to the location of the water molecules along the interface normal.