There was a good article on radiation risks of airline flights some years ago in the New York times. You can read a copy of the article here:
http://xray1.physics.sunysb.edu/~jac..._12jun2001.pdf

The story on radiation is this. In pre-technological times people would get around 200 millirem (mrem) or 2 milliSievert (mSv) of radiation per year from naturally radioactive rocks, cosmic rays, etc. This is maybe 300 mrem in modern times, with the extra radiation coming mainly from medical X rays, though at one point fallout from atmospheric nuclear weapons testing added 5-10 mrem to the mix. However, there is TREMENDOUS local variation, with higher dose at high altitudes (30 mrem/year extra in Denver?), local geological variations (more rock, or selenium in soil, or radon gas from radium decay, etc.).

At these low doses, the effects of slight increases in radiation are extremely small and therefore difficult to assess exactly. A good discussion is provided by the BEIR reports from the National Academy of Sciences, the latest of which is here:
http://www.nap.edu/books/030909156X/html
Another source is the International Commission on Radiation Protection (ICRP) which has a summary here:
http://www.icrp.org/docs/Summary_B-s..._1990_Recs.pdf

Your radiation dose in flight is due to a decrease in radiation shielding by having less of the earth's atmosphere above you to absorb cosmic rays. The dose rate depends somewhat on the routing. Flights near the magnetic north and south poles get more radiation because charged particles in cosmic rays are channeled towards the poles; that's why you see the northern lights. As a result you get more (double? triple?) radiation per hour on a New York to Tokyo flight than you do on a Los Angeles to Miami flight. Still, an average might be .5 mrem/hour at high altitude, so if you fly 100K miles per year (200 hours at altitude) you might add 100 mrem/year to your radiation dose, or about a third more than what you would otherwise receive from natural sources and from medical X rays. Another way to look at this is to use the BEIR and IRCP estimates that your cancer risk is increased by around 5% per Sievert, or by 50 out of a million per 100 mrem corresponding to 100K miles.

To put this in more perspective, if you smoke, your increased cancer risk is more like 5,000-10,000 out of a million.

It won't make much of a difference whether you sit at the window or in the middle, because energetic cosmic rays can plow through the skin of the plane without much problem.

My conclusion on all of this is that I don't worry about radiation when I'm skiing or hiking at high altitudes, and I don't worry about it on flights either.