Apple has released updates for Java SE 6 for all current versions of OS X today – OS X 10.6 Snow Leopard, OS X 10.7 Lion, and OS X 10.8 Mountain Lion. The update is is relatively minor, and aimed at improving security and overall reliability.
From the release notes:
Java for OS X 2013-004 delivers improved security, reliability, and compatibility by updating Java SE 6 to 1.6.0_51.
On systems that have not already installed Java for OS X 2012-006, this update disables the Java SE 6 applet plug-in. To use applets on a web page, click on the region labeled “Missing plug-in” to download the latest version of the Java applet plug-in from Oracle.
Please quit any web browsers and Java applications before installing this update.
See http://support.apple.com/kb/HT5717 for more details about this update.
See http://support.apple.com/kb/HT1222 for information about the security content of this update.
The update is available now through Software Update via the Mac App Store. Meanwhile, Sun Microsystems has also released updates to Java 7 for OS X, which are available for direct download through the Java download site.
