Ideally, the answer is have the film get hand inspected each time. Always.
X-rays are just like any other type of light for film - it exposes the film (and it gets through the film canister). You will occasionally see statements like "security check point that said film under ISO 800 would be unharmed going through the checked luggage x-ray machine" which is not completely correct. A better phrasing of this statement would be "film at ISO 800 speed going through this X-ray scanner once will not show noticeable effects in normal situations"
Key points there:
- Film of ISO 800 that goes through twice will
- Film of ISO 400 that goes through four times will (half as sensitive, twice as many trips)
- Film you intend to push process will likely have noticeable effects
- Normal circumstances does not include "we looked at it with more power because something else looked funny."
From the TSA web page: How to Get Through the Line Faster
Film. Pack undeveloped film in your carry-on bag. If you have film that is faster than 800-speed, tell a TSA officer who will manually inspect the film instead of placing it through the X-ray.
Note the carry on bag bit there. Higher power X-rays are used for checked luggage. If you believe you may have trouble, get a printout of that page. Also for travelers within the United States if you are really having trouble you may quote FAA regulation 108.17 (government printing office - pdf (page 335, second column, section e)):
If requested by passengers, their photographic equipment and film packages shall be inspected without exposure to an X-ray system.
All that said...
Consider getting a leaded bag. Note that the TSA does not advice this for US domestic flights (hand inspection is always an option so this causes more difficulties in these cases).
The TSA will (should) always allow for hand inspection of the film. Other countries may not and require the film to go through the scanner. A leaded bag (amazon) can help reduce the amount of exposure the film gets.
Having a leaded bag for your film (take it out before going through the scanner and inform the agent that this is a leaded bag with film in it) will have many TSA agents realize that its pointless to put this through the scanner and the hand inspection is the only option. This will not necessarily make them happier and may slow down the entire process (the bag will need to be inspected too).
Consider getting some high speed film (that you aren't likely to shoot) and carry it with you.
- I often carried some 3200 speed film with me when traveling on the off chance I was going to do some handled night photos. It also completely puts you in to the "this is high speed film" category that is well over 800 speed and so there is no question if it needs to be hand inspected or not.
- TSA: Transporting Film - Note that this is from the Wayback Machine and is a capture from June 2006 (most recent version of it) which describes what constitutes specialty film, mentions the cumulative effect of X-ray exposures and has some other tips that are good advice.
- Kodak: Baggage X-ray Scanning Effects on Film (lots of information and examples of what happens with different scanners)
- KEH: Tips For Traveling With Film