Yes, you should have some form of anti-virus software installed and running when connected to the internet. Not to do so is asking for trouble.
It's advisable to have an anti-malware solution running in parallel with an anti-virus program. Viruses and malware are not the same things.
Run on demand anti-malware software such as Malwarebytes Anti Malware, Spybot Search and Destroy and Lavasoft AdAware can be used in conjunction with an anti-virus solution to help keep your computer secure.
A good, configurable firewall will also help. Zone Alarm and Comodo are both free options which can be considered.
Paid for, all in one security suites are available form Mcafee and Norton, to mention just two, other options are available.
Whatever options you decide on, make sure the software is updated regularly, use real-time scanning where available and run regular scans.