Well, I'll chime in again with a useful post this time...
In regards to the H2O2 thing... That wouldn't do anything for efficiency. What electrolyzing pure water gives you is a stoichiometric (fancy word for balanced) mixture of Hydrogen and Oxygen. In an idea reaction 2 Hydrogen atoms react with one oxygen atom to produce one one water molecule. So you could theoretically use the gas produced by the water4gas device to fuel your engine with no additional air intake and you'd get nothing but water vapor out the tail pipe.
Most commercial electrolyzers have the two electrodes separated to keep the hydrogen and oxygen separate. The Water4Gas, OxyHydrogen, Brown's Gas, etc. devices let the oxygen and hydrogen mix. Because of that, you can't store the gas produced because of it's instability. If you hook one of these cells to your car you'd have to have a check valve in line to keep a possible backfire from reaching the electrolytic cell and causing a small explosion.
Brown's Gas has been used for years to make high-power torches used for working with metals such as platinum and palladium that will rapidly oxidize if heated with a regular flame. Brown's gas torches are pretty much identical to the device shown on the page. You've got a reservoir that holds water and a power source that runs DC current through it to separate the water into it's components and sends it immediately down the tube to the torch tip. The key to making it work well is to have a power supply that can generate enough current to keep the water electrolyzing fast enough to keep pressure to the torch tip but still slow enough to keep a significant amount of unstable gas mixture from building up in the cell.
So how does that all mesh with using it on a vehicle...
The hypothesis is that a car's alternator is constantly producing power that is not being used by anything. By pumping that power to an electrolytic cell it can be used to separate water into hydrogen and oxygen which is then fed into your intake and burned by the engine.
The place where the hypothesis falls apart is the "unused power" being produced by the alternator. Anyone familiar with power generation knows that when you put a load across a generator the motor driving the generator has to work harder to spin the generator at the same speed. This is just as true of a car's alternator. Every test I've seen shows the electrolytic cell pulling in excess of 20 amps of power. That power has to come from somewhere and it's going to come from somewhere. Now consider that in an ideal reaction the amount of energy needed to separate a water molecule into hydrogen and oxygen will be equal to the amount of energy released when the molecules recombine (combustion). With engine efficiency being only around 80% then there is no way an engine could provide enough power to supply 100% of it's own fuel.
But what about all the people testing these systems and showing all these great fuel efficiency gains???
There's a bit of voodoo going on behind the scenes. All of the W4G sites tell you that you need to fool your car's computer into cutting the fuel flow back so it can burn the H2+O gas. So these people go out and add these modules that tweak the voltage returned by the O2 sensor to make the computer think the engine is running rich. The result is that the engine leans out. That's where your fuel economy increases. Normally this would cause your engine to start heating up rapidly. Most engines have enough cooling capacity that they can effectively handle enough extra heat to give you some mpg gains through leaning the system.
There are a couple of other things that could be happening as well.... The burning H2+O gas produces water vapor that might conceivably add some cooling to the engine as well, but that may be more like voodoo than tricking the O2 sensor.
The other thing that is claimed is that there is a "perfect" electrolytic cell design that puts roughly 1.2 volts between each element in the cell and that magic voltage causes some sort of resonant reaction that drastically lowers the amount of energy required to split water molecules. Sounds like even more voodoo, but I haven't run the numbers myself so I'm just basing my assumption on common sense and accepted physics.
Now, if you could somehow use solar cells to charge up a bunch of batteries while your car is idle and use that power to run the electrolytic cell you might be able to run your car 100% on H2+O gas. Unfortunately with internal combustion engine efficiency being what it is you would be better served by using all that stored power to run an electric motor directly.
If you really want to look for a practical project to support that actually has pretty darn good chance of solving the world's energy problems once and for all, google polywell fusion or stop over to
Talk-Polywell.org and read for a while.