Violent galactic encounters or mergers are the leading contenders for triggering luminous quasar activity at low redshifts: such interactions can lead to the concentration of gas in the host galactic nucleus, thus fueling the suspected central supermassive black hole. Although optical images show a number of violently interacting systems, in many cases, the evidence for such interactions is only circumstantial (e.g., asymmetric optical morphologies, projected nearby companion galaxies) or not at all apparent. Here we image quasar host galaxies for the first time in the redshifted 21 cm line emission of neutral atomic hydrogen (H I) gas, which, in nearby galaxies, has proved to be a particularly sensitive as well as enduring tracer of tidal interactions. The three quasars studied have different optical environments that are normally seen around low-redshift quasars, ranging from a perhaps mildly interacting system to a relatively undisturbed host with a projected neighboring galaxy to an isolated and apparently serene host galaxy. By contrast with their optical appearances, all three quasar host galaxies exhibit ongoing or remnant tidal H I disruptions tracing galactic encounters or mergers. These observations demonstrate the utility of H I at revealing tidal interactions in quasar host galaxies and, combined with optical studies, provide a fuller understanding of the likely stage of the interaction.