It sure is common, but it's ignorant and I will always hate it. Knowing what "begging the question" means, and of course recognizing instances of it, is essential to a well-rounded education-- and independence of thought.
"Are you still beating your wife" is the classic instance of begging the question, which is to say asking a "loaded" question. There is an unproven or otherwise unacceptable term in the form of the question, namely the premise that the person being questioned-- ever beat his wife in the first place.
"Do you rob banks" is a covertly or implicitly loaded question even though it is straightforward in form-- unless you are posing it to a criminal suspect. To ask such a question "out of the blue" presupposes that the topic is germane to the person you're asking, and that the answer could conceivably be yes. That is an implicit presupposition.
When you beg the question, you also raise a question-- in the above examples the questions that are invited are, "why do you assume I ever beat my wife," and "what makes you think I'm the type of person who'd even consider robbing a bank-- is it a viable option in your lifestyle?"
The hotel clerk treats you rudely and asks you to prepay-- the man in line just ahead of you was fawned over and shown to his room like he owned the place.
"Why do I have to pay in advance, when he didn't?"
"Because you have no luggage, and such people aren't to be trusted-- they tend to abscond without paying."
"But I did have luggage-- some niggers stole it while I wasn't watching."
"Sir, if you wasn't watching-- how come you know it was niggers?"
Fallacious reasoning tends to turn communication into a vicious cycle of tit-for-tat.
Here's the site I usually recommend when the subject of begging the question arises on this forum. This fallacy is also called circular reasoning and vicious cycle, and goes by the Latin name petitio principii.
Yes, any premise in an argument that presupposes a term not yet established, whether it states that term or implies it, is "begging the question." Another way to look at it is, you're waiving a question that ought to be asked and answered, you're letting it slide.
In this case the question is, why would it ever be thought that I would steal a hot stove? Surely I'm smart enough to let it cool down first.
"Begging the question," when used properly, refers to making a circular argument in a debate by taking for granted the very question one is arguing about. I know that's a little unclear, so here is an example: Suppose that we are arguing about what type of government is best. You think that a dictatorship is best, and I think a democracy is best. I say, "A democracy is best because the officials are elected by the people." I haven't made any kind of an argument at all. I've defined what democracy is, but I haven't said why it's good that the people elect their officials. I'm taking the fact that it is good as an axiom, but if it were, we wouldn't be arguing! So I'm offering you an argument that basically asks you to accept as true the very thing we were debating in the first place, i.e. "begs the question."