Security Software...

Yes, Virginia, you definitely should, and quickly. And if you're using a Mac don't believe all that nonsense about how nobody makes viruses or malware for that.
They do, and they have, and there are security programs to guard against it.

And don't believe that you need to spend big money for protection. Some of the best free programs provide protection on a comparable level to some of their more costly competitors. For example, the free version of Avast among its other features includes an optional Boot Scan. This scan will search all of your files during a reboot or restart operation, and it works in between the time that your
active memory is unloaded on shutdown and is reloaded again during startup, so that means it can look at all your protected operating system files as well as everything else on your hard-drive while nothing is hidden from it. It can take a while to do its thing, but if you suspect a virus which hasn't shown in regular scans, this can dig it out. I've used it and it works.

Also, don't believe the story that you can only have one active antivirus program running on your machine, because there can be conflicts among them. Today's modern antivirus programs are mostly designed to be compatible with each other, and some can be run simultaneously if you wish. For example, I've run scans using Avast, Malwarebytes, and Superantispyware all at the same time, just to see if I could. They all worked very well and were quite compatible. None interfered with any other, and all completed successfully. Running more than one scan at a time though can take longer because it's using a lot more of your available resources. 

Why do that? Because some programs are better at finding certain kinds of malware than others are, so you may want more than one. Also, it makes a difference which browser you're using. Firefox has add-ons like Better Privacy
which can find and remove 'supercookies' called LSOs (for 'Local System Objects') that are like a cookie only bigger, never expire, are invisible to your regular cookie detection, can perform operations like a program would, and last but not least, they call home regularly with your personal data to report what you're doing and when and to whom. Without that add-on, you don't know if they're there or not, and I'll bet you they are. The first time I ran that add-on, it found dozens of them. So that's another side to security.

The old adage 'An ounce of prevention is worth a pound of cure' still applies. If you want a good security program, try Googling for 'Top Ten Free Security Programs' or something similar. Also, among those that cost you an annual fee, most have a free version which provides the most necessary basic protection without cost, so look at those as well. Surfing the web is like having sex - you shouldn't do it without protection.