Computer security is always an issue and it seems each day/month/year brings something new in the way of a threat. Having a good, up-to-date antivirus program installed as well as Windows firewall (or a third-party) firewall is often sufficient. However, these is only the basics, and there are other issues you need to be aware of.
Microsoft has put up a nice web page called “4 steps to protect your computer” and it provides links for learning about firewalls, operating system updates, antispyware programs and more. A good site to bookmark!
Be sure to have a look at "Basic Computer Security for the Home User" elsewhere here at WindowsTalk.