Basic science here guys. When you "burn" water, what are the waste products, hmmm? Are they, um, water? So let me see. I'm going to take water, do something magic to it--say split it into hydrogen and oxygen, and never mind where I get the energy to do that-- and then burn the hydrogen which combines with oxygen in the air to form water and release heat.

Yes, the hydrogen released from water can be burned (to form water again). Hydrogen really is the fuel and water is the product created when it is burned. Basic laws of thermo require that you cannot just make energy out of nothing. So you will never get more energy out of the hydrogen produced from water than what it took to create the hydrogen in the first place.

Water is not in any way possible a fuel. It never can be a source of fuel. Any device that uses a car battery / energy from the car's alternator (converts car's mechanical energy to electrical to recharge battery) will only be converting energy that originally came from the car's gasoline. Thus using such a system not only will not provide net energy in fuel, the conversion process cannot be 100% efficient due to thermodynamics laws and therefore will result in a loss of fuel economy.