In response to the question of why air is colorless, the chemist provides a very simple answer. It is only because the gases that make up air are all colorless. There might be some trace gases like chlorine and nitrogen dioxide, which are colored yellowish green and brownish red, respectively. But they are too dilute to make any impact, and air is effectively colorless.
However, physics provides a far more intriguing answer. It goes to the root of the question – what is color visibility, anyway? And the remarkable answer is that visibility is everything that a thing is not.
Take a good ripe tomato. What does it look like? Red. That is because the tomato absorbs all the light that falls on it except red light. In other words, the tomato appears red because it has nothing to do with red light. It is like calling a Spanish person Spanish because he knows every other language in the world except Spanish. Of course, this is absurd, but that is exactly how visibility works.
Most gases are invisible because they are very little capable of affecting light. Almost all the light simply passes through them. If there were dust particles hanging in the air, we would see them because they reflect some of the light falling on them (absorbing some of it and reflecting the rest, just like any other visible object). But the molecules are simply too small and too far spread apart to affect light in any meaningful way, and therefore these gases are effectively invisible, or colorless.
But this is only part of the answer. As already pointed out, some gases do have color, and therefore are able to absorb and reflect light. There are plenty of liquids, like water and ethanol, that are also transparent, and in liquids the molecules are far more closely packed than in gases. There are even solids, like perspex, that are transparent. (You cannot cite glass because physicists believe it to be a very viscous liquid.) The bottom line is simply the ability to affect light, and gases in general have the least effect.
But air is not entirely invisible either. People say that the sky is blue, but it is not really the sky but the air. Looking through a cubic kilometer of air will not detect any color, but looking at the entire atmosphere overhead results in a very strong tint of blue. The light is affected, after all, but not in the normal way of absorption and reflection. This is light being "diffracted." When light passes around a gas molecule it gets scattered. (It doesn’t bounce off it; the gas molecule is too small for that.) The blue comes from the fact that the nitrogen and oxygen in the air help to scatter blue light more than any other. (The carbon dioxide atmospheres in Mars and Venus make their skies red.)
However, physicists don't usually say that air is blue, either. They are at pains to explain this thing called diffraction, or scattering. But this is only academic. To point out why the tomato is red you need to explain light absorption and reflection. It is all a matter of how the light is affected by the object before it comes to the eyes.