I have Avast running, and use Malwarebytes and CCleaner periodically to scan and cleanout the computer.
I also use Mozilla Firefox with AdBlocker to surf the internet - I am always shocked at the amount of ads that are on Google and Internet Explorer the rare time I use those... usually to access a specific video or site that only uses those. AdBlocker is fantastic for reducing the advertisement pop-ups and blocks most spamware (similar to popup ads, just more annoying).
Most viruses and malware, as mentioned already, come in the form of something you click on to "open", usually disguised as from a friend or well known website. If it seem suspicious, don't click on it. All the "anti-virus" programs in the world will not help you if you actually click on / download the virus. They can warn you of a shady website, but you have to pay attention to the warnings.
There have been malware that disguise themselves as a Microsoft security program - those can be tricky, because they look legitimate. I know a few people who were caught by that.
Backing up / saving your information - YES! Do, and do it constantly. I used to pretend that I backed up my computers regularly, but finally admitted that I was lucky to remember to do it every few months, then realized that I was only doing once a year. Some computer geeks I know have hard drives that they back up to every day, but I never remembered to do it that often or even close.
I finally gave in and now use a paid "cloud" service that backs up our computers EVERY night automatically. I actually have used those backups a few times when getting a new computer, and if I accidentally delete a file. The cost of the service has certainly paid for itself. I use Mozy, but there are others - Carbonite, Barracuda, ect that all work similarly. You do have to keep your computer hooked up to the internet, but it works great for me. And save my rear end a few times!