Let's get the most obvious hoax virus alerts out of the way.
Banner ads are the worst offenders for the general Internet browser. These are those big things on the sides and tops of webpages with a large red x warning that "your computer may be at risk." Well, your computer may be at risk, but clicking on that ad won't do a single thing to actually make it any safer. Hopefully it won't shock you that clicking on that ad will lead to some bad consequences.
Another unfortunate category hits searchers trying to find a good antivirus program (for the record, we have a lot of reviews for free antivirus programs). It's pretty easy to make a somewhat respectable website and publish it. Therefore, some fake antivirus programs just exist as a website promising antivirus protection. These websites will convince you to just download their program through your own volition.
The worst may be a recent batch of malware that works through seemingly normal banner advertisements. Unfortunately, advertisements can sometimes be infected. Scripts in banner ads can be made to take advantage of existing exploits. This means that you may become unknowingly infected on a trusted website without engaging in any of the traditionally risky behaviors. If you are receiving hoax and fake virus alerts or other scareware notices without noticing anything abnormal in your past browsing, then this is the likely culprit.