Keeping your software up-to-date is an important part of securing your home computer. Vendors release patches or updates regularly to fix security holes that are found in their software. Keep in mind that you have to update both your operating system and the applications you use. Lastly, it is important to use software programs that are actively maintained.
Microsoft has a published timetable  for their support of Windows, Office, and other software they publish. Make sure the software you are using is at least in their "Extended Support Phase," which provides security updates. Windows 95, 98, and ME are no longer supported by Microsoft, and should not be used on machines on the Internet. As of August 12, 2010, these are the projected "retirement" dates for popular Microsoft products.
- Windows 2000 reached retirement on July 13th, 2010.
- Windows XP will reach retirement on April 8th, 2014.
- Windows Vista will reach retirement on April 11th, 2017.
- Windows 7 will reach retirement on January 14th, 2020.
- Office XP will reach retirement on July 12th, 2011.
- Office 2003 will reach retirement on April 8th, 2014.
- Office 2007 will reach retirement on April 11th, 2017.
Windows (or Microsoft) Update
Windows has a built-in updater that you can use called Windows Update or Microsoft Update. Windows update only updates Windows itself, while Microsoft Update will also update Microsoft Office and some other Microsoft applications. Windows Update provides a link to change to Microsoft Update. If you use other Microsoft applications, using Microsoft Update is highly recommended. You can usually find Windows/Microsoft Update on the Start Menu.
Windows also has a built-in feature called Automatic Updates. It regularly checks-in with Microsoft to determine if updates are necessary. If it finds updates, it automatically downloads them and may automatically install them as well, if it has been configured to do so. See this site  for instructions on how to configure automatic updates on Windows XP and this site  for Windows Vista.
Many applications provide their own automatic updates. You should follow their on-screen instructions when a message regarding an update appears. The most important applications to update are those that interact with the Internet, such as Internet browsers, browser plug-ins (like Flash or Acrobat Reader), email clients, file-sharing programs, or similar software. Most software will provide some instructions regarding updates in their help menu. At the very least, they will usually point you to their website so you may download the latest version.
Windows users at home may use Secunia's Personal Software Inspector . It scans your computer for known security vulnerabilities and provides some help in determining which applications need to be updated. This software is only for use on personally-owned systems, it may not be used on UNI systems or those of any other institution or company.
Update Links for Windows Machines:
http://windowsupdate.microsoft.com/  - Direct link to Windows Update
http://office.microsoft.com/officeupdate/  - Direct link to Office Update, which will walk you through security updates for Microsoft Office on Windows.
Apple provides updates for their current operating system and its preceding version. As of September 11, 2009, the supported versions of the Mac OS are versions 10.5 (Leopard) and 10.6 (Snow Leopard). All the previous versions do not receive updates for security vulnerabilities.
Apple provides a built-in updater for Apple products on the recent operating systems. It can be found by clicking the Apple in the top left corner and then choosing "Software Update." It will check for updates and walk you through the process of updating. By default, Software Update will check for updates on a regular basis and notify you of updates. Be sure to install the updates when prompted. This site  provides further instructions on using Software Update.
Many applications provide their own automatic updates. You should follow their on-screen instructions when a message regarding an update appears. The most important applications to update are those that interact with the Internet, such as browsers, browser plug-ins (like Flash or Acrobat Reader), email clients, file-sharing programs, or similar software. Most software will provide some instructions regarding updates in their help menu. At the very least, they will usually point you to their website so you may download the latest version.
As of December 11, 2009, the only version of Microsoft Office for Mac that is supported by Microsoft is Office 2008. All the previous versions do not receive updates for security vulnerabilities. Microsoft Office has a built-in updater that should be utilized regularly.
Most Linux distributions use a package management system that can provide updates. Some distributions will also notify you about security updates. It is recommended to install security updates regularly on Linux machines. Check the documentation that came with your distribution for more specific instructions and to check to see how long your distribution will receive security updates.