About a year ago I became a member of the elite few that actually know what this commonly (mis-)used phrase means. Ever since it's been driving me crazy each time I hear it because basically no one in the world seems to use it correctly. Most recently House MD said something like "which begs the question, what's killing this kid?!". So the writers can grasp hundreds of complex medical conditions and character interactions but still don't know the difference between begging a question and posing a question. It makes no sense.
http://www.whichbegsthequestion.com/defined/