Theoretically, once you've installed your anti-virus software on a clean PC, you should never have to scan it. Almost every anti-virus product worth its salt provides two main types of protection: on-access and on-demand. On-access protection provides continual monitoring of your computer, whereas on-demand is essentially a scan that you either run yourself or schedule for later (perhaps to run overnight).
If the on-access protection is any good, it should detect threats as they reach your computer. It can then repel them before they take hold. However, the worrying truth is that anti-virus software can be slow to react, which means a new type of threat may be able to worm its way onto your PC without your security product noticing anything amiss.
Eventually the anti-virus program may download an update that informs it about the malware now tunning on your PC. A scan could highlight its presence and aid its removal. Unless you are suspicious that a threat is active on your system, then scanning your PC once a month should be enough.
