thought it wouldn't take long for the "Its not Java, its the browser plugin, Java is perfect and can do no wrong". posts to appear.
Take a look at the list of affected products - scroll down a fair bit to the Java specific vulnerability list, particularly those marked with note 2:
Applies to client and server deployment of Java. This vulnerability [...] can also be exploited by supplying data to APIs in the specified Component without using sandboxed Java Web Start applications or sandboxed Java applets, such as through a web service.
Which means and Java program that responds to network connectivity, such as every Java server (and every Java client that talks on the internet) out there. So its not enough to remove the browser plugin, you need to patch Java everywhere. Everywhere.
Don't forget to patch your Oracle database, or Oracle CRM, Siebel, Peoplesoft, too... it has Java components that are affected. Oh yes, MySQL too which has 2 remotely exploitable vulnerabilities.