Once skepticle like you all, I once firmly believed that you couldn't see a laser beam shining through ordinary air without some sort of material [extra] to help scatter the light, no matter what color of laser it is.
The my brother bought a <5 mW green laser pointer, and I have seen with my own eyes, yes, you can see the beam through normal air.
But there are some limitations. In a brightly lit room, you can only barely, if at all see the beam. If you go outside into the black night (or even in a dark room for that matter), the beam becomes clearly visible and you can see it extend hundreds of feet down the street.
But in no way is it anything like a star wars "light saber", or like the pictures on that web site. Now accidents will happen, and I am told, [as is true for any laser, it is a bad idea to get it in your eye], when the <5 mW green laser hits your eye, for a while afterward, everything looks very milky white.
The reason why it is so visible compared to a normal red laser? I am not exactly sure. I have heard to theory that human eyes are mor sensitive to green light than red, which could be part of the reason. And/or perhaps because the green (532 nm) laser has a shorter wavelength than a red (635 nm) laser, allowing it to bounch off smaller objects suspended in air?