Thanks for the reply, boberonicus (nice name, btw). It's actually my wife's iPad. We've got a pile of chargers and cables, iPad, iPod, iPhone, and third party, so I've been checking to see if they work with my iPad, which they do, but they don't with hers all of a sudden. I did dig out the actual iPad plug/charger to make sure that it wasn't one of the others that was causing the problem, but really nothing seems to work.

Actually, as I write this, I have it plugged into a desktop and it is charging, though it states "not charging". That's good, but of course kind of impractical. We might have to call Apple support on this, but obviously if there is some well known--or not so well known--fix I'll take it!