I was in the USSR when Chernobyl happened, I changed planes several times to get there and back with both exposed and unexposed 400 speed 35mm film, there was a person with us that had 800 speed film as well. My film was X-rayed at every airport I went through, and twice at a few of them and my film, and my film was fine. The guy with 800 speed was fine as well.
That was probably as harsh as any average tourist is ever going to be on film.
FYI, you should be more worried about your film in the airplane than at the airport X-ray, I know this because some of the radiation detection devices I design can not fly or they will be contaminated. That sky thing is a really good radiation shield as it turns out, having less of it over you is not good for your film.