Manually download and install the latest Java update for Snow Leopard: http://support.apple.com/kb/dl1573
To see which Java Runtime Encviornment you're running, open the Java Preferences,app in /Utilities. The Java prefPane only applies to Java 7 in Lion and Mtn Lion.
Java Preferences can be found using Spotlight.
Update your Java 6 as previously instructed as it's supplies security fixes.
Java 7 and above is for 10.7 and above, Oracle is dropping support for Java 6.
However all versions of Java have been HIGHLY insecure, so it's advised not to use them at all
If your using Java based programs (like the free LibreOffice) then certainly disable Java in all web browsers and applets in Java Preferences.
Apple has a now annual OS X upgrade cycle that is causing havoc and disqualifying older, but perfectly working machines from running necessary software and dragging third party developers along.
So one shouldn't be running Safari (outdated and no Safari 6), Java 6, very possibly Chrome on OS x 10.6.8, but if you upgrade to 10.7 or above, your machine will perform slower and all your PPC based software will no longer continue to function.
It's sad, because OS X Snow Leopard has 1/4 OS X market share still and many can't upgrade because developers are not issuing 10.7/10.8 versions of their software because of AppStore and Gatekeeper signaling the closing of the operating system in the future.
The 10 year support cycle of Windows versions sounds like blessed relief compared to Apple's annual OS X upgrade nightmare.