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Hmm...the dog-hair question is interesting, but I think the X-ray machines are probably not the answer. If those machines were using THAT much ionizing radiation, you would have a serious ozone problem on your hands.
Instead, I think it has to do with the long journey your luggage takes. At the beginning and end of the trip it is travelling on conveyor bands made of heavy rubber. These could easily build up a nice static charge, that could attract the hairs. In the middle of the trip, the luggage is rubbing against all kinds of other bags, probably transferring the hair to its neighbors.
So my guess is that the hair ends up on or around the luggage bands, and on fellow passenger's bags.
Any other ideas?