A common mistake when confronting rumors is to repeat the damaging statement when defending it against it. "No, I did not beat my wife / drive drunk / steal that money / cheat on my taxes."
You have to confront rumors carefully. Here are some tips:
1) Always stay calm, no matter how horrible the rumors are.
Some attacks on a public figure's reputation are so outrageous and unbelievable that they work anyway by making the public figure lose their cool in front of the press or public.
2) Ignore common, everyday rumors.
There's always misinformation and talk. If you tried to correct every false rumor, you'd spend your days doing nothing else.
3) Let others defend you.
If a rumor attacks your credibility, everybody knows you have a vested interest in defending yourself. So does any spokesperson or PR firm in defending a client.
Whenever you can, have somebody else lead the counter-attack against a rumor, preferably someone with credibility and authority who can be seen as independent.
4) Refute big rumors quickly, before they fester.
Silence is interpreted as guilt. There used to be a 24-hour news cycle, and presidential candidates would set up War Rooms to make sure they had a response within each cycle.
Those days are over. The news cycle has been shortened to nano-seconds by blogs and the internet. Don't wait to respond.
5) You can't wound rumors -- you have to kill them.
Rumors will live on if you simply deny them. You have to provide an alternative explanation.
Kill a rumor by beheading its credibility. Give evidence of the truth with real support -- a document, video, audio, support from an independent authority such as a newspaper -- and go after the motive of whoever may have started the rumor.