An anti-malware software does not have to be installled on your computer, but it is a great tool to use as far as keeping your computer free from these nuisances.  Secondly at some point in time your computer will become a victim of a malware attack -- even if you have an antivirus software installed.  When your computer is affected by a malware program, the fight against the malware code will be much easier if an anti-malware software is installed.  Why?  Some malware, will prevent you from downloading or installing software once your computer is infected.  So if you have one already installed its just a matter of using it.

The most pesky malware, to me, are those fake pop up alerts that tell the user that their computer is infected with hundreds and hundreds of viruses, trojan horses, worms, etc. I had a client that was so disturbed by this, that she actually went out to purchase the software, which is exactly was these malware producers want to do.

The two anti-malware software I recommend installing are Spybot and Malwarebytes.  Spybot has been a long time favorite and is good at catching and cleaning a malware called Virtumonde, and Malwarebytes is a recent addtion for it's ability to clean out these fake alerts.