I think the only practical way you could truly run on water would be to use electrolysis to isolate the hydrogen then feed it back to a fuel cell to power an electric motor. Of course, the electricity you'd need for the electrolysis would exceed the amount produced in the process. Unless you had super high efficiency photo-voltaic cells to use sunlight to power the electrolysis, you can't beat the basic equation and produce more energy than you start with.
However, water injection can make a car more efficient. We used to add water (or water/methanol mixture, ie. windshield antifreeze) mist injection to the intake of racing corvairs to cool the air and increase the charge density. Since the engines ran very hot and pinged on the low-octane unleaded fuel available everywhere but at the racetracks, it did seem to help, at least in reducing the pinging and lowering the octance requirement to enable then to run on standard pump octane.