Well, this is a first for me on JWD - I somehow appear to have gotton a posting fight started without even knowing it was going down.
Here is the deal. There are some things that really should be self-explanatory to anybody with a basic high school background in first year physics and chemistry. One of these is that you can never get more energy out of a heat reaction than was there as potential energy in the first place. Potential (chemical reactive) energy in a jug of water is very close to nothing...the oxygen and hydrogen are already combined, and have released the heat in their separate states by combining. This results in steam - when the steam cools and condenses, you have water.
So, a quart mason jar of water is not going to mark very high up there on the potential fuel scale. It doesn't matter that there are two very reactive components there - i.e. hydrogen and oxygen. They would have to be separated in order to get fuel, and if you did manage to get them separated, it would take more power to do so than you can get back by re-combining them. Then, if you did put the hydrogen part into your engine, you would only have 2/18 * about 1KG of hydrogen - about 111 grams. That is if you could recover every little bit of the hydrogen...it is about the equivalent of maybe a shot glass of gasoline, to be very generous. But what is the point, if it took you two shot-glasses of gasoline to make it?
Another point is an interesting one - someone mentioned that maybe the hydrogen acted as some sort of "catalyst or additive" rather than as an actual fuel. For a long time, highly turbo-charged or supercharged engines have occasionally used a mix of water-alchohol in just that way, but it was not really a fuel in itself - it was more an internal coolant and detonation inhibitor (which allowed the engine to use more fuel and air from the normal sources without boowing up.) Very popular on piston aircraft engines in WW2. But for this to work to any advantage, you have to be overboosted to within an inch of explosion, and they did not try to split the water into molecular components.
And here is my argument to the "big business is evil and supresses this technology" line. If this held any hope of getting massive amounts of new-found energy, don't you think every hot-rodder in North America would have one on his SS396? Anything to go a tenth faster - that is the name of the game. What they do bolt onto their cars are superchargers, turbochargers, nitrous oxide bottles, and such. Not this, unless of course they are getting paid big bucks to stick on the decals.
Finally, no - I am not going to test this on any of my cars. The reasons should be obvious, if you have read my automotive posting history.
BTW - I don't think anybody mentioned that mythbusters did a segment on this and found no real effect. They got frustrated and Jamie put a direct hydrogen feed into the cars carburettor from a big pressure tank of pure H2. Naturally, it soon resulted in a satisfactory explosion.