After working tech support and also at a university help-desk, I can honestly say Firefox is one of the best things to happen to internet browsing in quite awhile. We used to hand out cd's with it to students who were having connectivity problems.
I've noticed Adware mentioned several times here - but SpyBot is another brilliant technology to wipe off malware:
http://www.safer-networking.org/en/index.html
In my experience, there are several basic steps that you can take to have *almost* no problems whatsoever with viruses and malware:
1. Do not use IE! I have always preferred Firefox for its ease-of-use, but Netscape and Opera are also fine alternatives.
2. If you use Outlook Express to check your email, you are also *dangerously* at risk. It, like IE, executes code without confirming with the user. Many, Many viruses are spread through just simply using Outlook Express. There are many alternatives out there: Eudora, Pine, Mozilla/Netscape Mail... The people who make Firefox also make an email client called Thunderbird - which is maturing quite nicely. Which you choose depends on your personal preferences, of course ;-)
3. Run Anti-virus! Well-rated vendors include Norton, McAffee, and Trend Micro's PC-cillin. If you dont have any money to spend - then free anti-viruses are out there. AVG and Avast are both highly-rated, and have been proven to catch many of the threats you will run into on the Internet.
4. Use some kind of malware-removing utility such as Adware, Spybot, etc... To be safe, you should run scans with both these utilities *and* your anti-virus around once a week.
5. If you have a broadband connection, you should really look into using a firewall. This will keep 'boogers' from being able to find you on while you are on the internet. It will also allow you to block things on your computer from being able to talk to the internet -- FYI: This is the reason when you get alot of spyware, that your machine slows down... It is using all of your machine's power to send malicious/tracking data through your internet connection. A firewall allows you to say NO to such connections.
Like OddTodd, I have had issues with some of the latest incarnations of ZoneAlarm, and I now use Kerio. It works very well. If you use it, you should know that it IS free, but has some things in it that you pay for after a certain time frame. These things include pop-up blocking and so on, that dont work as well as technologies found in most modern browsers like Firefox. So - if you use it, after awhile it will start telling you your trial period is fixing to end - but you can just ignore it. All it will end up turning off is stuff that was somewhat of a pain to deal with anyway - in my opinion :-)
I know it may sound like a pain learning about all of this, and having to run scans and whatnot -- but -- the internet right now is getting to be quite the 'wild west' if you know what I mean. If you don't take precautions, you *will* be taken advantage of. OddTodd was lucky - he knew what was happening, and was able to do something about it... some of the stuff out there right now will steal your personal information, and you will have no knowledge of it until it is too late (i.e. when you get in your Visa bill).