Your Anti-Virus program says your PC is malware-free. Should you get a second opinion?

 Your Anti-Virus program says your PC is malware-free. Should you get a second opinion?

Many computers are brought into my shop exhibiting all the classic signs of a malware infection, yet some of their owners insist that the problem can’t possibly be malware because they regularly scan their systems with an anti-virus program.
But when I run my own scans on those systems, I almost always discover that they are indeed infected, some of them with dozens of viruses, spyware objects, malicious toolbars and other nasties.