This is from the Kodak web site:
X-ray equipment used to inspect carry-on baggage uses a very low level of x-radiation that will not cause noticeable damage to most films. However, baggage that is checked (loaded on the planes as cargo) often goes through equipment with higher energy X rays. Therefore, take these precautions when traveling with unprocessed film:
Don't place single-use cameras or unprocessed film in any luggage or baggage that will be checked. This includes cameras that still have film in them.
If an attendant or security personnel informs you that your carry-on baggage must be stowed with the checked luggage or go through a second scan, remove your unprocessed film.
Have your exposed film processed locally before passing through airport security on your return trip.
If you're going to be traveling through multiple X-ray examinations (more than 5 times), request a hand search of your carry-on baggage. FAA regulations in the U.S. allow for a hand search of photographic film and equipment if requested. (See below for further FAA information.) However, non-US airports may not honor this request.
Request a hand inspection for all motion imaging origination films. Testing shows fog on motion imaging films even after a single X-ray scan. This increased fog flattens the entire toe region of the sensitometric curve reducing shadow detail in a telecine or projected image. However, Explosive Trace Detection instruments provide no risk to motion picture films and can be used in conjunction with hand inspection to provide a non-destructive method of motion film inspection.
If you're asked to step aside for a more thorough scan of your carry-on baggage, the film could be harmed if they use the more intense X-ray equipment.You should take your unprocessed film out of your luggage.
Lead-lined bags, available from photo retailers, will weaken the X-radiation on film and reduce potential harm. However, the effectiveness of any particular lead bag depends on the intensity and electric potential of the X-ray generator, the lead's thickness, and the film speed. If you use a lead bag, check with the manufacturer for the effectiveness of their products with airport X-ray devices. The inspection process may be triggered by a lead bag on the scanner screen. In a typical airport surveillance situation, the baggage may be pulled aside for additional inspection.
Consider shipping unprocessed, unexposed or exposed film through an expedited carrier, but first check with the carrier to determine what package examination procedures they are using.
Be polite, helpful and patient. Please remember that security personnel are trying to protect the traveling public.