When you see the coworker using your mug, casually sidle up to him/her and say, "Hey, whatcha drinkin'?" After receiving the response, you say, "Oh cool. Does it taste all right?"
At this point, your coworker will be puzzled, and will answer, "Yeah, it tastes fine [you idiot], why?"
You reply, "Oh, I was just curious. When I first got that mug, I started trying out this new immune-system-building strategy that I read about in [popular magazine you know coworker doesn't read]. Instead of washing the mug, you wipe two ounces of your saliva all over the inside and outside. It's supposed to prevent harmful germs from adhering to the mug. I noticed you haven't been out sick lately, so it must work! Cool!"