This topic has been debated here at RFF before (hotly debated). I'm just going to share my own firsthand, empirical experience. I am a sample size of one.
I have had film fogged after going through about 8 (8+) carry-on scans during a trip to eastern Europe. During the same trip I reserved some of my rolls for hand inspection through most (perhaps all) of these checkpoints. Those rolls (hand checked) had no fogging at all. E-chrome 100 and 400, B+W 100 and 400, and a little C-41 of un-remembered speed. The scanned films were clearly fogged, often heavily. Consistent with what I have been shown as examples of airport x-ray scanner fogging of photographic films. I'm convinced about the cause of my fogging. I should mention that it is un-contended that checked luggage (that which goes in the cargo hold of the plane) is zapped at much higher x-ray intensities. Your film is almost certain to be affected if it goes this route!
I have since learned that film with speeds above 800 are considered susceptible, and most B+W of moderate speed and above is also susceptible. I can also say that the number of times your film goes through these "harmless" carry-on scanners will influence susceptibility too! As a second experience to share: I have had my film go through the scanner twice (once each way on a trip from Oregon to Everglades and back) because I was too lazy to pull it all out for a hand check (not to mention the treatment I get from grumpy security people; not all, but some). I had no noticeable effects with those film. The only issues with those shots were "operator induced" and included poor exposure choice, poor composition, and flare effects from too much Florida Sun.
I say proceed with caution and make best-informed choices. Its certainly possible to let some films go through the scanners (a minimum number of times) with no noticeable effect. The trick is to know which films and how many times through the machine before you go through the hassle of "hand check". Add to that the reason for the film and you have another layer of decision making; vacation snapshots or paid assignment? Lucky for me, I'm rarely paid for my photographs. Lucky?
Remember: travel should NOT discourage the use of film. Be smart and it becomes a non-issue.