Fire up Software Update, and you're likely to find a Java-flavored update waiting for you. Apple has updated Java for both Snow Leopard and Leopard, releasing Java for Mac OS X 10.6 Update 5 and Java for Mac OS X 10.5 Update 10.
The Snow Leopard Java update "delivers improved compatibility, security, and reliability," Apple says, by upgrading Java SE 6 to version 1.6.0_26. The update addresses multiple vulnerabilities that could allow arbitrary code execution.
The Leopard Java update upgrades J2SE 5.0 to 1.5.0_30, and Java SE 6 to the 1.6.0_26 version for 64-bit Intel Macs. Apple says that support for "out-of-process Java applets" under Leopard is removed with this update. The update is only for Leopard Macs running Mac OS X 10.5.8 or higher; it too addresses multiple vulnerabilities that could allow arbitrary code execution.
Apple recommends quitting any Web browsers and Java applications before installing the update.