Hi,
I work in IT Security so I can add some value here. Java 6 is now deprecated by Oracle. That means no more security patches or updates will be released. Java 7 update 15 is the latest and secure version so make sure you are running that.
However, the actual vulnerability or threat itself lies specifically in Java applets within the web browser. If you are using Java to launch native desktop applications you are ok and one way to prevent these attacks would be to remove java from the browser completely - unless you use java applets (which is rare these days) you do not need your browser to be able to run java.
So if you have removed java in your browser and still use java 6 then you are not in bad shape. If you do need java in the browser then update to java7 u 15 and you will be ok - for now
See this link on how to remove java from your browser, please note, java in the browser is different to running java on your desktop and are treated as separate entities.
https://krebsonsecurity.com/how-to-unplug-java-from-the-browser/
I am happy to answer more security related questions on this or other topics so fire away!
Thanks,
t2w