As far as I am aware there is no Java browser plugin available for 64-bit linux users. I discovered (via senseis) that you can download the cgoban.jar file and run it locally.
wget files.gokgs.com/javaBin/cgoban.jar /usr/local/jdk1.6.0_10/bin/java -jar cgoban.jar
This works equally well for Windows, simply download:
and run it with Java by double-clicking on the jar.