Who's asking: Once again, Jennifer Lechner
Hell if I know.
No, seriously, this is one of those questions that can't have a definitive answer -- no matter what anyone says -- because none of us were alive when Jesus was around. But I'm willing to tackle this question, not as a theologian but as a close reader of the New Testament.
If we believe that Jesus was God as well as man, then he wasn't a sinner; therefore, he didn't break the third commandment (Exodus 20:7 -- "You shall not utter the name of Yahweh your God to misuse it"). So if we consider swearing to be taking God's name in vain, then no, he didn't swear.
But did he use vulgar language? I'm willing to bet that he did. He was a carpenter, after all, and he hung out with fishermen. Mark, the oldest of the gospels, reports that Jesus cursed a fig tree for being barren (Mark 11:14) and then that he drove the money-changers and pigeon-sellers out of the Temple (Mark 11:15). It seems reasonable to suppose that he spoke in language that would intimidate these people, and that may well have included words polite people considered bad language.
Mom allowed no bad language in her house, and I only remember her using a bad word once -- when she was cleaning Kathy's and my room, and pinched her hand in one of our desks. My language is not as clean as she'd like it to be, but I am always aware of my audience, and try to avoid bad language in front of children and polite company.
But it baffles me that so many people consider bad language to be a worse violation than other, much more serious offenses. I manage the e-mail that comes in to one of my clients' websites, and he gets more e-mail about the bad language in his books than about anything else. These books are thrillers, they're crime novels. They're stories of murder, mayhem, corruption, and all sorts of evildoing.
The readers don't seem to have any problem with that; what they object to is the swearing. Good grief.