You shouldn't if you can avoid it, especially for high-speed films (ISO 800 or above).
In the United States, FAA regulations require that "If requested by passengers, their photographic equipment and film packages shall be inspected without exposure to an X-ray system." (source: Section 108.17(e) of FARS.) After September 11th and the takeover of security by TSA in the US, some airport personnel try to tell you that this isn't true anymore. But the current TSA guidelines still allow for hand inspection. Keep a few high-speed films in your bag and tell the security personnel that you'll be going through more than five X-ray machines on your trip (x-ray exposure is cumulative for film, thus even though one pass of ISO 100 film through the X-ray machine isn't harmful, multiple passes can be). This makes it difficult for them to stonewall you. If they do, ask to speak to a supervisor, and ask that supervisor to show you the current TSA regulations regarding hand checking of film. It helps to be polite and to facilitate such searches. I always carry my film removed from film canisters (which I pack in my checked luggage) and in a clear bag that I present at the security checkpoint, making it as easy as possible for the security personnel to view the contents.
If you arrive at the airport security checkpoint with film in boxes, they will be opened. If you arrive with film in canisters, often the security personnel will open one or more to check to see if there's film in them (that's even true of the clear Fuji canisters!). If you ask them to hand inspect your camera because it has film in it, you will be required to show that it is an operative camera, so make sure that you've got fresh batteries in it! They may even require you to take a picture, or if film is not in the camera, to open the back.
Note that TSA personnel now ask the question "do you have any film in your checked baggage" when you drop it off at the X-ray station (if the bag gets checked and taken at the counter, they often don't ask this question). That's because the machines used for checked bags can be cranked to higher power to see inside, and it's likely that your film will be fogged if they do.
Note that X-ray machines outside the US aren't always regulated in terms of "exposure" they produce on film. It is common to find X-ray machines outside the US that can impact film lower than ISO 800 with a single pass. I consider it especially important to insist on hand checks for film outside the US for this reason.
