Java seems to have some security issues affecting Linux as well as other operating systems. The issues specifically affects the Java browser plugin, not the Java installation. I haven't used a Java website for ages, and in fact when I checked, I didn't have the plugin installed in this installation (Debian Wheezy). Worth checking if you do have the vulnerable plugin installed, and either disabling it or restricting use to sites that absolutely require it. Brian Krebs has the details, but here are some useful links.
Check to see if you have the plugin installed.
How do I disable Java in my web browser?
Firefox: Protecting Users Against Java Vulnerability