Nobody seems to understand the reasons why yet, but if you use Firefox 3 and JRE 6 update 11, Java Applets won't work. This has something to do with FF3 itself, because the same JRE will work with FF2.
The workaround is to go into the Java Control panel, Advanced, and turn off the next-generation Java Plugin.
If you're on Vista (sucks to be me), the Java Control panel may be hidden behind the Start/Settings/Control Panel/Additional Options icon. If you're REALLY unlucky and are running an x64 version of Vista (kill me), you may have to click on "Show 32 Bit Control Panels" after you click on Additional Options.
There are also some IE Options/Internet Options that you may need to turn on - something about allowing local scriptable content.
Ask me what I hit my head on all day long today. Go ahead, ask...