There is some controversy about full-body airport scanners. The two concerns fall into categories of privacy and public health. I will focus on the health effects. There are 2 types of scanners, X-ray and microwave. Since I did my MSc in nanotechnology with a focus optics, I can't help but think about these 2 different sources in terms of their physical effects on human tissue.
On the one hand, a single x-ray photon can ionize an individual atom, (rip an electron off). When ionized particles are created inside cells, they can create oxygen radicals and other nasty charged particles, which can cause cancerous mutations. At very low doses, x-rays have no measurable effect since the body can clean up most mutations, but at high doses or consistent medium doses, they can cause cancer (see Fukushima for details). The airport x-ray scanners are not routinely tested by an independent body, and we therefore have to accept the claim of the manufacturers that the doses are not harmful. I for one do not, and neither do a large number of UCSF Professors: http://www.npr.org/assets/news/2010/05/17/concern.pdf
As for microwave scanners, these emit lower wavelength radiation. The wavelength is so low that an individual photon can only heat up a large molecule, not ionize it. This means that I would feel perfectly comfortable standing in front of a microwave beam. Well, not perfectly comfortable but at least I wouldn't have to be worried about cancer:
So if I get stopped at the airport and pulled aside for an x-ray scan I'll say no, microwave scan: go ahead. What about you?