No, no, no! "Beg the question" is NOT the same as "raise the question."

According to A Dictionary of Modern English Usage, to beg the question is "the fallacy of founding a conclusion on a basis that as much needs to be proved as the conclusion itself."

My definition of this phrase is correct because I am the ultimate authority on the subject.

There, I just begged the question.

Want more? The alt.usage.english FAQ covers it extensively, and includes the following paragraph which nicely explains the etymology of the phrase (and also quotes Aristotle, which is always a handy tool for shoring up an argument):

The Latin term for the fallacy is petitio principii, a translation of the Greek to en archei aiteisthai="at the beginning to assume"; but aiteisthai does literally mean "to beg". The phrase can be traced back to Aristotle (4th century B.C.): "Begging or assuming the point at issue consists (to take the expression in its widest sense) in failing to demonstrate the required proposition. But there are several other ways in which this may happen; for example, if the argument has not taken syllogistic form at all .... If, however, the relation of B to C is such that they are identical, or that they are clearly convertible, or that one applies to the other, then he is begging the point at issue." (Prior Analytics II xvi)