The Department of Homeland Security has warned about Java and had this suggestion:
Disable Java in web browsers
This and previous Java vulnerabilities have been widely targeted by
attackers, and new Java vulnerabilities are likely to be discovered.
To defend against this and future Java vulnerabilities, consider
disabling Java in web browsers until adequate updates are available.
As with any software, unnecessary features should be disabled or
removed as appropriate for your environment.
Starting with Java 7 Update 10, it is possible to disable Java content
in web browsers through the Java control panel applet. From Setting
the Security Level of the Java Client:
For installations where the highest level of security is required, it
is possible to entirely prevent any Java apps (signed or unsigned)
from running in a browser by de-selecting Enable Java content in the
browser in the Java Control Panel under the Security tab.
If you are unable to update to Java 7 Update 10 please see the
solution section of Vulnerability Note VU#636312 for instructions on
how to disable Java on a per-browser basis.
Re: Are we in trouble?
It depends on the user's knowledge. This exploit seems to be a social engineering exploit and therefore may need active co-operation of the user to succeed. It's quite possible that a moderately savvy user can retain an active Java and not fall prey to the current exploit.
What about all those applets for network manager and the other stuff on the top right side of our screens? Will they vanish if I remove Java?
Not all applets have to do with Java. Applet could just be a diminutive term. This definition may clear your doubts:
a small application program that can be called up for use while
working in another application
Also, how do I know which Java is on my computer?
Check out How can I tell what version of Java I have installed?