I turfed Tycho off my computer chair so I could sit at the computer. He stalked off to get some food. A couple of minutes later he was right behind my chair, apparently playing with one of the castor wheels. He wasn't making any noise, so I ignored him, apart from a mental note not to roll the chair backwards without checking where he was.
A minute or so later, he was still there, restless but quiet. It's an odd place for him to be, so I spun the chair without moving it, to take a close look. Turned out the long fluff at the end of his tail was trapped beneath the wheel. It can't have hurt him, since he didn't say anything (and he's let me know when I've trodden on his tail). I must have been within an inch of the bones at the tip of his tail. I moved the chair and he wandered off, no harm done, fortunately.
I guess computer chairs are the modern day equivalent of the old saying: "As nervous as a long-tailed cat in a room full of rocking chairs".