Your checked baggage and your carry-on baggage get x-rayed at least once.
It does, but the x-rays used for checked luggage are of a much greater intensity than those used for hand luggage. The ones used for hand luggage will have little to no effect on most film. Slide struggles more, as does film with a higher ISO rating. Last time I went away my film (Portra 400VC) went through five x-rays when it was unexposed and then another five exposed. There was not a hint of damage and I think I had eighteen films in all. The chances of getting your film damaged using a high street photolab compared to getting them ruined by an airport scanner must be close to 100:1.
You can also ask for hand inspection if you want. They can refuse, it depends who you speak to. If you have a lead bag they will often re-scan it, doubling the chance of it getting shagged (particularly if you have no idea of the effectiveness of the bag). If they're suspicious they will get it out and check anyway.
It always strikes me as being absolutely pointless using one. Just walk up with the films you have and ask for them not to be scanned if you're really bothered. If they say yes, it will set your mind at ease. If they say no, there's fuck all you can do about it. Putting those films in a lead bag at this point would just make them suspicious. I already look borderline homeless and like I'm on a different planet, I do not need to bring any more attention my way, particularly seeing as I have something in my knee that will set off the metal detector without fail. I often have prescription painkillers with me as well. I don't think I've ever got through security in less than ten minutes. Faffing about with lead bags will not help my cause.