If you have 64 bit installation of Windows Vista it is usually a problem to use plugins that run on 64 bit. However when using a 32 bit browser version, like Mozilla Firefox 3 it should not be a problem to make use of a 32 bit plugin.
However when installing JRE 6 the plugin will not be recognised properly after installation. To overcome this you have to do the following after the installtion of the Java Runtime Environment from Sun.
Copy the following files from your JRE installation (e.g. C:\Program Files (x86)\Java\jre6\bin) to your Firefox plugin location (e.g. C:\Program Files (x86)\Mozilla Firefox\plugins):
(the first one might be already there).
Then applets should work fine with Firefox.
Hopefully Sun will soon provide a proper 64 bit Java plugin for 64 bit systems.