Apple has managed to issue a fix to the vulnerability that plagued Mac systems in the recent Flashback malware attacks, but this fix is only supported in select versions of OS X, and will not include Tiger and Leopard. The two updates released by Apple for the Java runtime in OS X will nudge the Java release to the latest version, which is 1.6.0_31. The updates will be made available to OS X 10.6 and 10.7 systems which already have Java installed, and you will be able to make the update on your system via the Software Update utility in the Apple menu. It is rather unfortunate that there are no updates to patch older versions of OS X, including Tiger and Leopard, leaving you vulnerable to Flashback.
Having said that, if you happen to run an older Mac, you will need to be more creative by taking alternative steps to protect your machine. Folks who have an Intel-powered Mac will be able to make the upgrade to at least OS X Snow Leopard, and go ahead with the most recent Java patch. As Apple no longer sells Snow Leopard, you ought to be able to find it online, via Amazon or eBay for instance. If you cannot upgrade your system, then just disable Java in the meantime, and you are good to go. As usual, it is always prudent to pay closer attention to safe browsing practices whenever you are connected.