Nitrogen Tire Inflation for Street Cars: Stupid

Unless you have a bottle of N₂ laying around, or you get Nitrogen free without an increased price somewhere else (like higher valve stem prices), don't bother putting nitrogen in the tires of your daily driver.

Why?

Argument 1: Oxygen leaks out because it's a smaller molecule. Then your tire is under-inflated
Counter: Check your frikken tire pressure!
Bonus counter argument: When the O₂ leaks out, you refill the tire with . . . 78% N₂ (air). Over time, the concentration of Nitrogen inside your tire increases because you replace missing Oxygen with Nitrogen-rich compressed air.

Argument 2: N₂ does not damage the insides of your tires/wheels/etc. like Oxygen does.
Counter: The outside of a tire is subjected to more Oxygen than the inside (see Argument 1) as well as Ultraviolet radiation. The outside of your tire is going to break down WAY faster than the inside. Unless you are filling your tires from an OXYGEN bottle, don't worry about it.

Argument 3: The water content of compressed air, even with a moderately-efficient dryer on the lines, is putting liquid water in your tires. This causes pressure variations with temperature, potentially causes corrosion in the valve stem, and is generally Bad.
Counter: See Counter-argument for Argument 1. In addition, the amount of water vapor in your tires is miniscule. If you did somehow manage to end up with liquid water in your tire, it would actually tend to help balance the wheel/tire combination.
Counter: If you don't replace your valve stem when you replace the tire, you are asking for trouble anyway. The amount of corrosion build up in the valve stem during the service life of your tires is nothing to worry over. If you have so much water in your air that it causes rim corrosion, you are doing something pretty drastically wrong (like using gas station air pumps).

Argument 4: NASCAR and IndyCar teams use Nitrogen in their tires because it helps them more accurately predict tire inflation.
Counter: They also run engines for several hours at a speed that would make your engine explode, if it ever spun that fast for a second. They also drive 200MPH and those drivers can feel a 1 PSI change in tire pressure. You can't feel the 10PSI missing from your left-rear tire right now. This is not an argument that applies to street driven cars.

Argument 5: Airliners use nitrogen so their tires don't have ice in them.
Counter: You will break up any significant ice in your tires when you are leaving your driveway. If your tires have ice in them, then weather and road conditions will be such that the ice on the road should be 1000 times more worrisome.

With proper tire inflation, you will have increased fuel efficiency, better handling, longer tire service life, and increased safety. This is not an argument for or against refined N₂ in your car's tires. It is a set of good reasons to check your tire pressure every month, at least, like your car's manual says to do.

If your tire shop makes a Great Big Fuss over how they can sell you Nitrogen in your car tires, smile at them and say "no thanks."