A recent flight to Los Angeles had great results. Halfway through the flight the pilot announced he was dropping from the 38,000ft cruising altitude to 30,000ft to avoid persistent turbulence (in my notes I wrote 36,000ft but it can be difficult to hear what the guy was saying, and I think the data shows a better match to 30,000ft). The data were taken once a minute.
I also added to the graph a yellow line showing the background rate in my office which is 7.5 microrads/hr. So flying at 38,000ft gives you a rate about 40 times greater than here in my quiet little office in Chicago.
I've previously done this on trips to Los Angeles: Dean W. Armstrong: Geiger Counter
In the past I've also looked at potassium salt, Pentax Takumar lenses, dinosaur bones, and have a live report of radiation rates from my office.