There are four possible reasons for this result:
Cause #1:
The most likely reason for this behaviour is that you do not have Java installed on your computer.
Test
your Java Virtual Machine (JVM)
You can download and install the Sun Java plug-in at this address:
http://java.com/en/index.jsp
Cause #2:
Another possible cause for this behaviour is that you do not have Java enabled on your computer.
To verify if this is the case, do the following in Internet Explorer:
Select the Tools Menu -> Internet Options -> Advanced Tab
Once you are in the Advanced Tab of the Internet Options dialogue box, scroll down to the setting for: Microsoft VM.
To enable the Microsoft VM check the "JIT compiler for virtual machine enabled" checkbox, this requires a restart of the browser, not the computer:

You can also optionally select the "Java console enabled" checkbox which will allow you to see any error messages that may be produced by the Microsoft VM.
Alternatively, if you have the Sun version of Java then find the Java (Sun) entry in the list and check the "Use Java 2 v(version number) for <applet>" checkbox, this requires a restart of the browser, not the computer:

If you do not see either of these options listed, then you do not have Java installed. Please refer to Cause #1 above.
Netscape and Opera ship with Java but it needs to be explicitly selected for installation during the browser installation.
Cause #3:
The third possibility is that you have both Microsoft and Sun's versions of Java installed and enabled on your computer and they are conflicting with one another.
To solve this issue, follow the steps in Cause #2 and select only one version of Java to use; Sun's or Microsoft's.
Cause #4:
The final possibility for this behaviour is that your version of Java may be corrupt.
To solve this issue, uninstall your current version of Java (if possible) and then download a new version from Sun following the instructions contained in Cause #1.