Any time you browse the internet, open an email or open a file on your computer, you're at risk of a potential virus or trojan infection. If you don't recognise the email address, or don't know where the file came from, standard advice is don't open it. While antivirus products aren't necessarily perfect, and are generally retroactive when it comes to protection, they do provide a a little more security to help in keeping your machine secure. This page has links to various vendors of security software for you to choose from.
Some people believe that Antivirus solutions aren't worth bothering with and they'll never be infected if they're not stupid with what they do online, and this may well be true to some extent. Even sites you consider safe can be compromised, so if you don't want to go belt and braces, you should at least consider some form of protection.
For those that don't like living on the edge, most will have their favourite Antivirus/Internet Security products that they'll recommend. Of course, these recommendations are all subjective (mine included) based on their usage/knowledge of the product. Before you buy a product, take a look around for reviews. I tend to look at the Virus Bulletin website as they do regular comparatives of the major (and not so major) vendors. A subscription may be required for certain aspects of that site. There are many other review sites out there just a search engine click away.
For those that aren't aware, if you're running a recent version of Microsoft Windows, you already get basic protection in the form of Windows Defender.
Right, on with the list ...
ESET - Widely acknowledged as one of the leading Antivirus solutions around today. Free trial available.
Symantec - Norton Antivirus. Love it or hate it, you've probably heard of it. Tends to come bundled with new computers. Free trial available.
McAfee - Another well known Antivirus vendor, and another that has many that love it and just as many that don't. Free trial available.
Trend Micro - Currently touting their 'Ransomware protection' products. Free trial available.
Panda Security - Not one I've ever used myself (although I could say that about lots of software products). Free trial available. They're also offering a free antivirus via their Cloud Antivirus website.
Grisoft - AVG. Seemingly the first thing that pops into everyone's head when asked for a recommendation. I suspect purely for the fact they offer a cut-down free version of their Antivirus product.
Avast - Another well known brand offering a cut-down free version of their software.
Avira - Adding to the list of free and paid versions is Avira AntiVir.
Comodo - More free offers to keep the thrifty people happy. Paid version also available.
ZoneAlarm - Well known for their Firewall product. Antivirus also available.
Malwarebytes - Last but not least and used by millions as an extra layer of defence. Malwarebytes seems to be pretty much a standard part of the toolkit for most. Available in both free and premium formats.
So there you go. It's not a complete list. As with most things in the technology age, there's new products coming out all the time and for multiple different types of device.