Paul is correct that one advantage of nitrogen in aircraft tires is the lack of flammability. Another is the much misunderstood (and mostly irrelevant in the case of cars) goal of avoiding moisture induction when servicing the wheel and tire assembly.
Unlike cars, an aircraft may start it's day in 100*F+ tropical temps with 100% humidity and end it's day in -40*F arctic conditions. Enroute, the ambient temperatures can be in the area of -50 or -60*. Any moisture inadvertently pumped into the wheel ass'y at point of departure would most likely turn into a solid lump of ice.
At touch down, the still frozen wheel will be required to go from zero to 150+mph in less than a second. Any imbalance could throw braking performance or handling off severely.
A big, big reason it's used and completely overlooked by the tin foil hat brigade is simple logistics. Many aircraft are serviced out on the ramp far way from an AC outlet to plug an air compressor into. It's much simpler to have a cart with bottles of nitrogen to wheel around and much simpler to recharge those bottles with nitrogen than maintaining a separate fleet of dry air bottles.
Many aircraft wheels are made of magnesium- the corrosion factor with this application is not comparable to steel or aluminum car wheels.
Again- if it's free, why not. Other than that, I'll take my standard 78% mix that I also use for breathing.
