I just followed the instructions
here to update to Java Verion 6 Update 16. I created links in /usr/lib/mozilla/plugins and /usr/lib/firefox/plugins. It's all very easy and the test shows I am now running the latest version of java which I wasn't before.
In a nutshell I just downloaded the self extracting archive version, chmod +x the download, su to root,cd /usr/lib, run the download. This creates a new java install in /usr/lib/jre1.6.0_16/ for the most recent version. I then deleted the existing links and recreated new links in the browser plugin directories.
