Listen to whatever is being said without getting too emotional or losing your temper. You don't know what message will get sent back through the grapevine. If the information is accurate, don't go on a witch hunt to find the leak. You can't close the grapevine down, but you can put a crimp in access to it. If the information is totally false, don't make a public denouncement.
Nothing cuts a grapevine deeper than a completely false story.
Pump as much accurate information into the system as you possibly can. Prevent rumors by consistently leveling with employees. Correct false rumors immediately. Communicate in person whenever you can. Memos, e-mail messages, and comments that get passed through numerous people are usually wide open to interpretation.