Both you and Racer have this 100% wrong. As Magiver said unless you use a water seperator water will be delivered to the air nozle. I have seen impacts spew a stream of water in some cases. This BTW is in LA which is not known for it’s humidity.
When I was a technician I ran my own water seperator which I placed between the shop air source and my air tools. You would be amazed at the amount of water that came out.
OK I’ll buy the water in the air deal.
But there is another reason to use air. As we have seen in the James Bond movie, if your car goes into the water, you may be able to get a breath or so from letting air out of the tires 
Nitrogen filled tires lose pressure about 30-40% more slowly than air filed tires. This is because the permeability of oxygen through rubber is 3x to 4x that of nitrogen. The rate is so high, the mere 20% atmospheric O2 concentration causes air-filled tires to lose pressure significantly faster than nitrogen-filled tires.
Since low tire pressure significantly hurts gas mileage, all other things being equal (initial pressure, check interval, etc) nitrogen filled tires will (from a fleet average standpoint) produce better mileage. If you check and correct your tire pressure every week, then nitrogen probably doesn’t make any difference.
Since O2 leaks out faster than N2, won’t air-refilled tires automatically over time become mostly nitrogen-filled? According to this reasoning, O2 diffuses out faster, and air refills are about 80/20 N2/O2, so eventually the tire would be mostly nitrogen-filled.
However some basic calculations show the rate of change is so slow your tires will likely be replaced first. Tires lose pressure at about 1 psi per month, which equates to 5% volume, according to gas volume calculations. Airing them up once/month results in approximately 1% increase in nitrogen the first month. With each successive month the rate of nitrogen increase diminishes. In fact it will never be pure nitrogen since you’re always adding 20% O2.
What about Helium? Helium has much higher permeability through rubber than either air or nitrogen. That’s why helium party balloons lose pressure so quickly. For the same reason that nitrogen helps mileage on average, helium would hurt mileage. However if you checked and corrected your tire pressure every day, helium would probably not lower mileage.
There are various arguments for using nitrogen in tires. For regular cars, and assuming unchanged owner maintenance behavior (IOW they infrequently check tire pressure), modestly improving fleet average mileage seems a valid advantage. However if owners would regularly check their tire pressure, nitrogen seems to have no gas mileage advantage over air.
Great links, dude, thanks! 
From that techcentral link:
"In a tire filled with compressed air, the oxygen molecules tend to “migrate” through the wall of the tire over time. That’s why, when you open the garage to check on your aunt’s dust-covered 1980 Pontiac the tires are often flat.
But nitrogen molecules migrate 3 to 4 times more slowly than oxygen, so tires stay properly inflated longer. There are other benefits. Nitrogen retains less heat than oxygen and therefore allows tires to run cooler."
I’m skeptical and would like to see a cite. As others have pointed out, O2 molecules are larger than N2 molecules, and would permeate through apertures more slowly as a result. This, combined with O2 only being 22% of what’s in the tire in the first place, any difference at which they “migrate” would be even less significant.
I call urban-legend-snake-oil-hooey, unless someone can cite an alternative mechanism for this phenomenon.
As you’d expect, diffusion rate of O2 and N2 through various membranes has been studied for over a century, and is well understood.
Diffusion rate is defined by Fick’s Law, and is dependent on the frictional coefficient of the molecule, not just its physical size. The frictional coefficient is based on (a) Stokes Radius (not physical diameter) of the molecule, and (b) The viscosity coefficient of the gas at the given pressure and temperature. I’m guessing that N2 has a greater frictional coefficient than O2, due to either greater viscosity and/or larger Stokes Radius than O2, and that probably explains the lower diffusion rate.
The equations to calculate these are complex, but it’s not snake oil. If any physics major is reading this, they could probably give more details.
If a tire filled with plain air leaks oxygen faster than nitrogen, as you add air over time to keep the tire inflated the proportion of nitrogen will increase and the proportion of oxygen will decrease. I don’t know what the exact numbers are with respect to the rate of loss of different gases, but if there’s a big difference between nitrogen and oxygen I’d expect the proportion of oxygen in the tire to approach 5% pretty rapidly. That is, it would quickly get to the point where the oxygen content would be insignificant.
Some of us…coughcough…have pointed out the correct version: that O[sub]2[/sub] molecules are actually smaller than N[sub]2[/sub] molecules.
I don’t know if this is the direct reason for oxygen’s higher permeability through rubber or if it’s a coincidence. But the fact remains, if we’re worried about molecule size at all, oxygen is smaller.
As mentioned in my above post: http://boards.straightdope.com/sdmb/showpost.php?p=7590292&postcount=23 basic calculations show the tire will wear out and be replaced before it gets mostly filled with nitrogen by this method.
Ahh, thank you, I stand smarter.
Although the equations look to be of empirical/statistical origin as opposed to being derived from fundamental physics principles. But that is similar for most gas laws anyway.
If empirical measurements have shown that O2 diffuses more rapidly than N2, then though I will have to eat my prior words, I’m still not paying more to fill my tires, by gum! Cheap free air, like nature intended.
Also, according to this web site, molecular motion is a key factor in determining diffusion rate. It discusses helium vs oxygen, but nitrogen vs oxygen is likely similar: Re: Why does helium leak from a latex balloon faster than oxygen?
Any science teachers or educators: This would be a good opportunity to experimentally demonstrate a topical issue: is there an observable basis for lower leak rates of nitrogen-filled car tires? You could fill a regular balloon with O2, one with N2 and maybe one with Helium and empirically measure the leakage rate. Depending on the class level, this could be analytically backed with math.