Anti-Virus scams

Have you ever been surfing the web and found yourself looking at a convincing looking anti-virus scan of your computer running on your screen, which tells you that you're infected with numerous viruses? It's a scam!
The anti-virus "program" is just an animation on a web page, the virus infections non-existent. The idea is to scare you into paying for a fraudulent (scam) anti-virus program devised by the Eastern-European Cyber-Mafia.
These fake anti-virus pages are served up by hacked web sites, hacked advertisements on web sites, or by "poisoned" Google search results: you can come across them browsing perfectly legitimate sites.
As well as trying to con you into thinking your computer is infected, most of these pages will also try to infect your computer with a Trojan horse by means of an exploit. This is a way of installing malicious software on your computer without you clicking 'yes' to anything. (A drive-by download.) If your computer is not 100% up-to-date and secure, you could end up with a scam anti-virus actually installed on your computer, and they are very hard to remove.
How can you deal with these scam anti-virus attacks, and stay safe from rogue programs?
Keep all web-facing software on your computer up to date. This includes browsers and multimedia applications like Flash. The best way to do this is to use Secunia Personal Software Inspector- it wil scan your computer for out-of-date software and provide a download link for a security update.
If you do then come across a fake anti-virus scan on a web page, ignore the scam and close the browser tab or window.
Security Fix has more information.
If you are unlucky enough to get infected with a scam anti-virus program, your best advice is to try Malwarebytes' Anti-Malware or SUPERAntiSpyware Free. Both programs are free to use- although paid versions are also available.
UPDATE: Readers of the New York Times website have seen such a scam, as reported here.