The X-rays won't damage the tapes, but the magnets used in the equipment might. However, this is a theoretical problem. In practice, I have sent luggage containing video tape through no end of airport X-ray machines - some in out of the way places where they'd have no compunction about turning the dial to Max - and suffered no detectable deterioration.
I suppose you could always slip a few tapes in your pocket if you were paranoid (and you'd got exclusive footage of the aliens landing!) Otherwise, don't worry.

-Pete