According to R&D Magazine, researchers at UCLA have discovered that peeling Scotch Tape generates X-rays. Apparently, quite a lot of X-rays, if you're doing the peeling in a vacuum. The scientists built a device that peels Scotch tape from a roll in a vacuum chamber at the rate of 1.2 inches per second, which generates short bursts of X-rays (about a billionth of a second long each) from where the tape is being peeled. Electrons jump from the roll to the sticky underside of the tape that's been peeled away; when they hit the sticky side they slow down and generate X-rays. UCLA has filed for a patent on this technique, which could be used by paramedics to generate X-rays in the field.
Using your office tape dispenser is safe, according to these researchers, but I wouldn't stand too close if I were you.