It's already been stated but cannot be overstated. The first rule is carry your film in your hand baggage, and never in your checked hold luggage.
The x-ray machine used to examine hand baggage is much less destructive, and even today the operators are familiar with most film formats. These machines are designed to scan 800ISO or 1600ISO film multiple times without causing damage. I've personally had a roll of Delta 3200 go through no fewer than seven different airport hand baggage scanners and no damage done.
The scanners for checked luggage are more powerful and your bags are often subjected to more zaps from various angles as the machines look for naughties. You really can have film ruined in checked baggage. A whole day's shooting on the TV show Lost was ruined this way. The process is automated or semi-automated so there's no human to look and say "Oh, there's film. Let's stop zapping this suitcase".
X-ray and other radiation damage to film is indeed cumulative, so the more airports you go through and the more times your film is scanned, the more damage is done. So if possible, reduce the passes through the scanners. In the USA you have the right to have security hand inspect your bags, but they often don't actually like being asked. However, what I have done is noted that my bag was going for a second go through the scanner and politely asked "Rather than have it go a second time could you look by hand? There's photo film in there". Be pleasant, and calm and the security people are usually OK with you.
Don't make the mistake I did a couple of years ago and have a camera loaded with film in your hand baggage. I got pulled for an extra check and the security guy said he clearly knew what it was, but he really ought to see the back opened before he could let me through. In the end I talked my way out of that, but you may not be so lucky. If you're planning on shooting out of the window, load your film on the runway.
Don't bother with the lead lined film pouches. The lead will shield your film from x-rays but then the security staff cannot see what's in there. They see a mystery box, which they will then zap more times and likely pull your bag for extra checks and demand to know why you've got a lead lined box in there.
Although most x-ray security staff seem to still be familiar with film (they've laughed at my super 8 camera in hand baggage), some may not be...especially with large format sheet film etc. They all know what a 35mm or 120 roll looks like, but a box of sheets may or may not provoke extra interest. Be prepared to explain, calmly, what it is.
The Kodak link above is still useful as it refers to the scanners introduced right after 9/11 in US airports (mostly bought second hand from European airports who had already been using them). The same basic system is still in use.