Here's what you do.

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!"

Coworker will never use the mug again.

What mudpuppie said.
In fact, I'm thinking of bringing in a mug and hope that someone tries to use it, just so I can use this.

Or, you could make a mug that says "I AM AN IDIOT" or "I EAT POO" or "EVERYBODY LOVES RAYMOND, ESPECIALLY ME" on it, so people will avoid the stigmug.

mudpuppie, you are a sick, sick person. I knew there was a reason I liked you.

I need mudpuppie to be my office mate so we can pull all kinds of pranks.