Most of the damage done to us by ionizing radiation, such as X-rays and gamma rays, are not a consequence of direct hits to our DNA, but are a secondary effect of the radiation splitting water into highly reactive and destructive molecules - the oxygen free radicles. It is these oxygen free radicles that then go on to damage our cell's vital components, like DNA. Water is by far the most common molecule in our bodies, and statistically will be the most likely thing hit by an energetic photon of radiation that strikes us.
The oxygen free radicals are molecular species, such as the extremely reactive hydroxyl radical (*OH), as well as hydrogen peroxide (H2O2) and the superoxide radical (*O2-). These are often called oxygen free radicals, but not all of them are technically radicals (having an unpaired electron), so reactive oxygen species is really a more appropriate term. These reactive molecules can then oxidize susceptible places on the DNA that lead to mutation. Hydroxyl radical, is by far, the most reactive of the bunch, and basically reacts immediately with whatever is in it's way as soon as it is formed.
1=singlet oxygen (higher energy state), 2=molecular oxygen, 3=superoxide radical, 4=hydrogen peroxide, 5=hydroxyl radical.
A common site of damage is the oxidation of the nucleotide base guanine (G) to produce 8-hydroxyguanine, also known as oxoG. Whereas, normal guanine will base pair with cytosine (C), oxoG can base pair with both cytosine and adenine (A). If oxoG happens to base pair with A, then after the next round of DNA duplication there will be a point mutation from the original G:C to the newly mutated T:A. It turns out that this particular switch is very common in many tumor cells, and may be due to the damaging effects of radiation.
Oxo-G forming an inappropriate base pair with adenine
In this way, the effects of radiation are mainly by turning your own water against you. In addition to radiation, oxygen free radicals are produced just by normal metabolism. As we extract energy from sugar molecules, we pass electrons down the "respiratory chain - a set of enzymes in our mitochondria, that eventually react with Oxygen to form water. During this process, free radicals are produced that have the same effect as those produced by water's interaction with radiation. It has been estimated that in just one year of breathing - something we all have to do if we are alive - is the equivalent of 10,000 chest X-rays worth of radiation. Just being alive is dangerous!
1. "Oxygen: the molecule that made the world", by Nick Lane. See chapter 6 (Treachery in the air) for some of the stats listed. (a really great book, by the way).
2. "Molecular biology of the gene", 7th edition, by James Watson;
Also an awesome text.