Everyone should have an up-to-date real-time anti-malware application running on their system at all times. These programs won't guarantee that you will never get infected by a rouge application (e.g. virus, Trojan-horse, worm, root-kit, etc.), but it provides better protection then not having this software running at all.
If your computer starts acting strangely, you might want a second opinion to see if your system is actually infected. This is why there are offline virus scanners for checking your system for malicious software.
There are several vendors that offer this type of software, but one of the newest is from Microsoft and called the Windows Defender Offline. Below is excerpt from the site: "Sometimes, malicious and other potentially unwanted software, including rootkits, try to install themselves on your PC. This can happen when you connect to the Internet or install some programs from a CD, DVD, or other media. Once on your PC, this software might run immediately, or it might run at unexpected times. Windows Defender Offline can help remove such hard to find malicious and potentially unwanted programs using definitions that recognize threats. Definitions are files that provide an encyclopedia of potential software threats. Because new threats appear daily, it's important to always have the most up-to-date definitions installed in Windows Defender Offline. Armed with definition files, Windows Defender Offline can detect malicious and potentially unwanted software, and then notify you of the risks."