I had the same problem. I guess the java from apt-get just isn't good enough. So, I downloaded from Sun but that didn't work either. It worked for my Firefox but, not for Azureus.
Solution:
You need check your java installed.
If it's not the newest version of java you need to get it.
http://java.sun.com/j2se/1.5.0/download.jsp
Pick the self-extracting that isn't a RPM.
Build the package.
Code:
fakeroot make-jpkg sun-j2re1.5_1.5.0+update09_i386.bin
If you don't get any errors move on.
Install.
Code:
sudo dpkg -i sun-j2re1.5_1.5.0+update09_i386.deb
Set the new java install as default
Code:
update-alternatives --config java
Pick the one you just installed if it isn't already picked.
You're done Azureus should now work.
Some how people can get Azureus to work with the plugin and not have to go through the process of installing and configuring JRE 5.0 with the update. For the rest of use this should work.
Source:
http://www.azureuswiki.com/index.php/Java