If someone's always mouthing off and just can't shut up, they've got logorrhea, a pathological inability to stop talking. Sounds better than "loudmouth."
As its sound suggests, logorrhea is related to diarrhea — an inability to stop something far more unpleasant from flowing. Diarrhea comes from two Greek words put together, dia meaning "through" and rhein meaning "to flow." In the case of logorrhea, the log prefix is from the Greek word for "words," meaning literally "words flowing through." Technically speaking, logorrhea is an actual illness, unlike such similar terms for extreme chattiness such as loquacious or garrulous.