The idea stems from the fact that underinflated tires increase rolling resistance, adversely affecting fuel economy (among other things). Any gas mileage improvement through using nitrogen in tires would come from nitrogen's reported ability to maintain tire pressure at the correct level for longer, because nitrogen is supposed to leak through the walls of the tire more slowly than oxygen. Well, perhaps, but air is already about 78 percent nitrogen, so devotees won't really realize a huge benefit from switching to pure nitrogen. Not only that, but leakage is likely to be more significant at the tire bead or around the valve than through the body of the tire.
Other nitrogen benefits are sort of "inherited" from its use in aircraft tires, truck tires and race car tires. (If it's good for the pros it should be good for us, right?) The use of nitrogen is required in the braked wheels of aircraft over a certain weight, because the inert gas reduces explosion risk under combinations of extreme loads and high temperatures that far exceed the conditions experienced by car tires. As an inert gas, nitrogen may also extend the life of the tire carcass - important if tires are retreaded, as is common for trucks and aircraft, but insignificant for car and light vehicle tires, where tread wear determines longevity. Racers know that the most important benefit of using nitrogen is that it is "dry" - the water vapor in compressed air causes too great a pressure change as the tire heats up, a big deal when a half-pound of air pressure change can affect the handling of a racecar at the outer limits of performance.
The bottom line? Nitrogen is no substitute for checking your tire's inflation regularly. If it's free, go ahead and use it. If you have to pay for it, save your money.
[N2Revolution via CNET]