Now let's see what Wikipedia says about hydrogen boosting: 

"Hydrogen fuel enhancement can be optimized by implementing established lean burn concepts, and at minimum to achieve an actual increase in gas mileage the air/fuel ratio needs appropriate modification."

"At minimum to achieve an actual increase in gas mileage the air/fuel ratio needs appropriate modification" (it needs to be leaned down). With fuel-injected cars this modification can be done with an EFIE (electronic fuel injection enhancer) for minor leaning, but I know a way to lean it down as much as 30%. 

Fact : To achieve more gas mileage it is essential to lean out the fuel mixture. A carburetor equipped car needs to have the carburetor leaned down. Fuel injected cars need something more costly than an EFIE.

Plans for building an EFIE that can decrease the fuel injection by 2.5% maximum is at http://better-mileage.com/memberadx.html and the electronic device can be bought from Eagle Research for $60.

You can lean the air/fuel mixture down until just before your car runs rough at idle. See http://www.foxflying.com/engine_leaning.htm Hopefully you can get it down to 20% or 30% lean which is an air/fuel weight ratio of 17.5:1 to 19:1. By only adding oxyhydrogen to the engine you can't improve gas mileage. The carburetor or fuel injection system has to be changed. Actually you don't even need added hydrogen with a 30% leaner mixture. Only around 60% (and more) may cause misfiring. See graph:

Below is a graph showing how oxygen sensors change their voltage output (0 - 1000mv) according to the oxygen level they detect in the exhaust. When the sensors output goes below 200mv (.2v) with a "lean" condition, the computer will have the injectors inject more gasoline to richen the mixture. When the sensors output goes above 800mv (.8v) with a "rich" condition, the computer will have the injectors inject less gasoline to lean down the mixture. Unfortunately this minimum to maximum response is only from 14.2:1 to 14.9:1 air/fuel ratio which is only 2.5% from the center at 14.55:1. An EFIE will interrupt the voltage line from the oxygen sensor that normally goes to the cars computer to send its own voltage output to the computer. It can be set to trigger off any voltage level from the oxygen sensor between 100mv and 600mv.  But the most you can lean down the air/fuel ratio with it is around 2.5% which isn't very much.  Around 17:1 gives the engine the best thermal efficiency. This is a 15% reduction in gas used. But a lean 17:1 mixture normally has too slow a fuel burn-time which may cause knocking and misfiring. 

Questions and Answers

Why use a hydrogen booster at all if the main gasoline saving is from a leaner air/fuel mixture?
It may be useful for insuring ignition of fuel at very lean mixture ratios. A typical hydrolyser can't make enough hydrogen in order to truly speed up the combustion flame but its small hydrogen output may be enough for some ignition enhancement.

How much hydrogen/oxygen is needed from the hydrolyser?
My car tests show that .21 LPM hydroxy was better than 1 LPM hydroxy (see details below) as a supplement to a true fuel leaning system. It may be that very small amounts of hydroxy are enough for ignition enhancement. (It could also be that the hydroxy I added to the intake had no benefit at all. I hadn't considered that possibility and so didn't test without it.) Obviously, larger hydroxy production rates put too much of a strain on the engine and lowers gas mileage (unless the alternator is of the old style). Engines with a lot of "torque" for hauling loads will not be affected near as much as commuter cars by the engine strain caused by the alternator supplying extra current to make hydroxy.

What about potential damage to my engine?
I am a member of the share groups of Yahoo on this subject and no one has complained of any damage to their vehicle (although few people in those groups have installed a hydrolyser). For one, less than 2 liters of oxyhydrogen is not enough extra fuel to raise the engine temperature significantly. As long as your cars engine is not knocking, misfiring or backfiring the engine should be safe.

My testing for engine temperature increase showed a 5 degree Fahrenheit exhaust temperature increase at idle in drive from 120 to 125 degrees with .2 LPM oxyhydrogen (3 amps) and Carburetor Enhancer addition which is a 4% increase in temperature. The rise was only one degree when just the carburetor enhancer was turned on. Measuring the exhaust temperature like I did is a good way to see what effect the changes are having.

The only other potential damage is valve and exhaust pipe rusting from the byproduct of oxyhydrogen combustion, which is water. But at the minimal levels of oxyhydrogen addition there is very minimal extra water. Some water normally comes out of the exhaust of normal cars anyway which is a normal byproduct of burning gasoline. Fortunately gasoline always has corrosion inhibitors in it.

I normally get around 20 mpg in-town. Here's the in-town test results of trying oxyhydrogen on my Honda Accord :

oxyhydrogen           Ignition Timing              miles per gallon
 none                      advanced                        20.1 
.5 LPM                   advanced                        15.7
.25 LPM                 standard                          20.9
.2 LPM                   delayed                           16.25

I had just bought the car and didn't know that the ignition was advanced about 10 degrees until after I tested it with 1/2 LPM . 

NEGATIVE REPORTS FROM MEMBERS OF HYDROXY YAHOO GROUPS:

I have made a Smack's Booster and am getting a lot of hydroxy gas
but my first check of mileage actually revealed a drop of about 2-
3mpg. I have read that some cars may detect the cleaner emissions
and assume they need to inject more gasoline, so apparently that is
what mine is doing. I know it is a matter of finding what will work
for tricking my car into using the hydroxy and improving mpg.

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Mileage loss of 17%. Not enough HHO produced for a large block 8cyl
engine. Will probably need to build a second unit. Thinking of setting
my timing back to original setting if HHO is not making a big
difference in the fuel mixture at present. Will post results when
positive change is achieved.
-David

My comments: The first guy has the misconception of the cars computer injecting more gasoline to compensate. He needs an EFIE or programmable oxygen sensor, but not for the reason he thinks. The second guy, David, got a 17% mileage loss because he changed the ignition timing. If he'd left it at the standard setting he probably would of noticed little or no gas mileage change.

6-27-08 test results of using a Carburetor Leaner for in-town driving:

I drove 32.2 miles and refilled with 1.57 gallons for a resultant 20.5 miles per gallon which is about normal for this car anyway. Most of the engine-run time for this test was warming up the engine and the start and stop of in-town driving. I doubt anything can improve mileage much for this type of driving. The Carburetor Leaner only reduces gasoline consumption when cruising and decelerating which for this type of driving is a minimal percentage of time.

6-28-08 Hydroxy and Carburetor Leaner HIGHWAY TEST
Test Car: 1985 Honda Accord, 1.8L 4 cyl engine, 3 barrel carburetor

Temperature/ Mileage Tests With standard engine setup:

Engine
Temperature (*)             Miles         Gas used            MPG
513°                                 31.4            .925 gal               33.9

* (Peak engine temperature was read at the end of a long flat stretch of road after the engine had already reached its maximum temperature since leaving the gas station.)
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Modified setup with .17LPM hydroxy + Carburetor Leaner  

Engine
Temperature         Miles       Gas used       MPG
553° (+7.8%)         31.4           .86 gal            36.5 (7.7% more than normal)

Conclusion: Significant mileage increase is due mostly to Carburetor Leaner. The hydroxy is useful though to prevent misfiring. Strangely enough the percentage mileage increase is almost exactly the same as the percentage temperature increase. 

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TEMPERATURE TEST
547° without modifications
567° (+10%) with .17 LPM hydroxy

Conclusion: Adding hydroxy alone causes 20° hotter running because .17 LPM adds to the fuel energy used by this engine. This fuel increase, which burns quickly, leads to higher peak combustion temperatures.

TEST PARAMETERS
All the tests after the in-town mileage tests were done the same evening on the same flat road going an average of 55 mph. Refilling was done at the same gas station on the same pump with the car faced the same direction (in case the cement had an inclination). The temperature tests were done on the westbound part of the road against a 10 mph headwind. A thermocouple was inserted into a rust hole in the exhaust pipe before the catalytic converter and taped in place with aluminum tape which covered all the hole. This thermocouple was connected via a 5 foot cable to my digital voltmeter (near my feet where I could easily read it) with temperature readout. The thermocouple was designed for use with this voltmeter. Hydroxy was added to the intake stream at the inner air filter housing between the air filter and carburetor opening.

CARBURETOR LEANER
This modification in its basic kit form is very good but can be even better. More mpg can be had by electronically turning it off when the rpm's are below 1500 so that it won't ruin the cars ability to idle. Another way is to open the valve more during idle so that it idles roughly. Then adjust the idle fuel mixture screw for a richer idle mixture so that it idles smoothly again.

7-05-08 Hydroxy and Carburetor Leaner HIGHWAY TEST
Test Car: 1985 Honda Accord, 1.8L 4 cyl engine, 3 barrel carburetor

Temperature/ Mileage Tests With  .21LPM hydroxy + Carburetor Leaner set to max (*)

Peak Engine
Temperature                  Miles         Gas used            MPG
527°                                 29.3            .71 gal                 41.3 (+21.8% more than normal)

* (Manually controlled Carburetor Leaner was set with the valve open so far that the engine barely kept running at idle and did die a couple of times. Soon I will make it electronically controlled so that it only turns on when the rpm's are above 1500.)
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Modified setup with 1.2 LPM hydroxy + Carburetor Leaner set to max 

Engine
Temperature                Miles       Gas used       MPG
557° (+5.7%)                 29.3          .789 gal          37.1 (9.4% more than normal but 10.2% less than the 41.3 of the previous test run)

Conclusion from both runs: Too much hydroxy gives less gas mileage. The Carburetor Leaner leaned out the air/fuel mixture even more this time which gave better mileage in conjunction with the hydrolyser when set to minimal production of .21 LPM. Obviously it doesn't take very much hydroxy to prevent misfiring. 

Watch Out for SCAMMERS!

You need to be careful about what you buy and from who. For example, here are two samples of valid discontent: 

I ordered a ******** from www.*********** for $264 approximately July 1st of 2006. I waited 9 weeks to get it. On Sept. 7th it finally arrived. It was homemade and cheaply made. About an 8” piece of black ABS with a cap on each end and two 6” bolts with two washers on each of them. I couldn’t believe some one would try to sell this crap for $264 dollars. Gas production was almost non-existent, I didn’t measure it but I would guess about 2 liters per hour, by how slowly it was coming out. I tried to return it and was told…… NO REFUND! I had a text conversation with the seller and apparently he is “A LEGEND IN HIS OWN MIND!” I would rate this device as JUNK. Don’t waste your money.

The ******** has been revealed to be nothing more than the same CRAP sold by **********. It was purchased and disassembled for inspection by some people in another Yahoo group. (watercar group I believe). It consists of 2 stainless pieces of threaded rod with washers mounted on each and that is supposed to be worth $300-400 dollars? If you feel like being made a sucker, buy one! Otherwise learn from what others have experienced.......

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Hey, I'm not the only person saying that hydroxy alone usually will not effect gasoline savings:

quoted from http://www.brownsgas.com/allyouneedtoknowaboutbrownsgasfuelsavers.html
"If your vehicle has an oxygen sensor and you use the air-intake system you could install a lambda control, otherwise no fuel savings at all."

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http://www1.eere.energy.gov/vehiclesandfuels/pdfs/success/plasmatron-ld-dec01.pdf 

talks about the Plasmatron Fuel Converter which converts some of the gasoline to hydrogen/etc to increase engine efficiency by up to 25%.

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from http://www.repairfaq.org/filipg/AUTO/F_Gasoline7.html#GASOLINE_009

What is the effect of changing the air-fuel ratio?
For a given engine using gasoline, the relationship between thermal efficiency, air-fuel ratio, and power is complex. Stoichiometric combustion ( air-fuel ratio = 14.7:1 for a typical non-oxygenated gasoline ) is neither maximum power - which occurs around air-fuel 12-13:1 (Rich), nor maximum thermal efficiency - which occurs around air-fuel 16-18:1 (Lean). The air-fuel ratio is controlled at part throttle by a closed loop system using the oxygen sensor in the exhaust. Conventionally, enrichment for maximum power air-fuel ratio is used during full throttle operation to reduce knocking while providing better driveability [38]. An average increase of 2 (R+M)/2 ON is required for each 1.0 increase (leaning) of the air-fuel ratio [111]. If the mixture is weakened, the flame speed is reduced, consequently less heat is converted to mechanical energy, leaving heat in the cylinder walls and head, potentially inducing knock. It is possible to weaken the mixture sufficiently that the flame is still present when the inlet valve opens again, resulting in backfiring.