At least a bit of research seems to have been conducted on this. I chased a few results down the last time the subject came up here. In short, the scanners used to check carry-on luggage produced no visible damage in film below 800. The machines that scan checked luggage use a different technology and are much more powerful. No film was found to escape damage from their scans.
There are a couple of variables in all this. One is how well a given machine has been maintained and how well it is calibrated. Another is the fact that the impact of the scans is cumulative. I.e., chances of visible damage increase as you put the film through multiple scans.
In my own experience, with 100, 400 and 800 film, I've seen no damage from carry-on scans on trips that included up to six scans.
I've never used a lead-lined bag, figuring that obviously hiding something from security crews is a bit pointless. They might pull the film out and hand check it. Or, they might pull it out and send it through the machine again.
Going by anecdotal reports here and elsewhere, requests for a hand check of film may or may not be successful. I've seen a number of posts that say requests for hand checks will not be entertained at any major UK airport.
Finally, for folks flying international routes into Washington Dulles: After recently flying into Dulles on an international flight, I was tagged for a secondary customs inspection. This entailed putting every bag I was carrying -- including the bag with the exposed film -- through a scanner of some sort. I saw no damage when the film was processed and scanned.
[ADD: The trouble with research on this (which ought to be dead simple to do) is that different airports use different machines, and the condition of any given machine must be a factor. How often are carryon machines calibrated? If a machine starts to emit abnormally high levels, can the operator detect that, or will it only come to someone's attention during periodic maintenance? Do operator skills have any impact? Are older faulty machines scrapped or sold to other airports?]
