Current research
I've just stumbled across this forum and i'm very interested in some of the posts. There is a lot of misinformation generally on this topic and plenty of debate even amoung the "informed".
I am a physicist working directly in this field so i'd just like to clarify a few fundamentals: the radiation dose received by aircrew (and some frequent flying passengers) is indeed typically higher than workers at nuclear power stations - this is in large part becuase their dose is much more closely monitored and controlled. It is true that the dose received is not something to panic about - typically two to three times the average UK background level - but it is not true to say that it is unimportant. European legislation recognises air crew as radiation workers and airlines typically apply rostering to avoid exceeding an operational threshold which would require them to apply regular health checking.
This all primarily relates to cosmic rays. The additional hazard from some types of solar flare has only recently started gathering momentum in terms of industry awareness. Radiation from the largest of these flares can not only cause personal dose to exceed annual limits (though one of these has not occured for over twenty years) but they can also pose a threat to avionics via radiation effects on microelectronics. The radiation environment is mixed and complex and most radiation dosimeters do not adequately measure the dose (this includes TLDs incidentally). Altitude and latitude are the most important factors but inverse square law has no relevance at all.
Concorde was obliged to carry a monitor because of its high altitude, but in fact the dose on a subsonic flight between London and LA is higher than the dose on Concorde because of the higher latitude and greater duration. CARI-6 mentioned in another post, is a standard tool used for establshing dose on flights, but it is far from perfect and does not apply to solar flares. Research in this field is ongoing but awareness is poor.
Apologies for the lengthy post but I hope this clarifies a few things. For further information google "Advances in Measuring and Modeling the Atmospheric Radiation Environment" for a recent article and there are other papers. The European Cockpit Association published an open letter on this topic in September 2009 and this provides a reasonable summary.
I can provide further information to anyone who is interested - the more awareness this gets in the industry the better, especially as the legislation does not currently mandate any monitoring of frequent flying passengers.