It irritates me that, this term is used as if it's the same as "raise" or "prompt" the question. It isn't.
"Begging the question", if I understand correctly, means to advance an argument on the basis of a premise that is essentially the same as the argument itself, or at least just as much in need of justification.
So if you say, "I know he is telling the truth, because I know he doesn't lie" that's begging the question.
It's a useful, if a bit quirky, phrase whose usefulness will be lost if this sloppy usage continues.
Oh Somebloke, the world is divided between that tiny minority who know that 'begging the question' is to assume a point is proved, and the rest of the world who use it to 'raise a question'. Even people like John Humphries say it incorrectly. So when I saw it used properly on MN a while back it gave me much joy.