Play this one right, and you'll not only scare them away (although it will often manifest in their storming off in a huff) but they will steer clear of you.
Often such behavior results in absolutely nothing else happening. But even -- let's say in a work environment -- if the person runs off to tattle, you have a defensible (and articulatible) position.
Now granted this advice is predicated on the assumption that you weren't actually breaking policies, laws, or seriously screwing the pooch.
RTWT. My own usual response to "I'm offended!" is "Sucks to be you." But Mr. MacYoung's method might be a bit more diplomatic.