Today Apple released their Java update for users of OS X 10.6 Snow Leopard. It is listed as 'Java for Mac OS X 10.6 Update 12'. The version of Java provided is 6u39, AKA Java 1.6 Update 39.
Apple's Java update is available via Software Update from within OS X 10.6.
For the moment, you can also download 10.6 Update 12 at the link below. HOWEVER, please note that ALL the information on the page is WRONG and out-of-date. (0_o) Hopefully this will be corrected by the time you visit the page. For now, only use the page for the download link! Ignore everything else and just click the 'download' button:
At this time, there is no security information available about this update at Apple's website. Apple has so far failed to update their 'Apple security updates' page with this update. (0_o) Hopefully they will have caught up with themselves by the time you visit their security page:
Thankfully, Apple has emailed the security details about this update, which I have provided below: