Apple released Java updates for Mac OS X 10.6 (Snow Leopard) and OS X 10.7 (Lion) and 10.8 (Mountain Lion). The update brings Java SE 6 to the most recent version.
Apple hasn't added the updates to its Support site as of this writing, but the patch notes in the Mac App Store in Mountain Lion say:
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.
When Apple does release the patch notes on its Support site, they should appear as such: