NOTE: This is not just a bug for Mac OS X. Windows is also vulnerable if QuickTime is installed!
Initial reports were that the bug required that Safari be used to go to a certain website, however current reports (unconfirmed but reasonable) indicate that the problem is in Java handling in QuickTime, that any Java-enabled browser is a viable attack vector, if QuickTime is installed, and disabling Java stops the vulnerability.
While the Opera browser has not been confirmed to have this bug, it’s far better to be safe than sorry. (So far the specific details of the bug have not been released.)
Until the bug is fixed, you can easily disable Java in Opera, either by going to Preferences → Advanced and then clicking on Content. Uncheck the box next to Enable Java, as shown here:
or press F12 (or Alt + F12 in Mac OS X) to bring up the quick preferences window and disable it as shown here:
(Note: screenshots are from MacOpera, but WinOpera will look largely the same.)