I regularly listen to Steve Gibson's Security podcasts and Steve's recent podcast explains alarming problems recently discovered with Java. Security experts are recommending you remove Java or at least don't let it run from your browser. Here is a PC World summary explanation of the problem. Note: this problem applies to any machine with Java (Windows, Mac, Linix).
Windows: Removing Java from Windows machines is pretty easy. Just to Add/Remove programs and remove all instances of Java. Most versions of Windows come with Java already installed.
Mac OS X: Recent versions of OS X don't come with Java installed but Java will be installed if you've said yes to web sites that use it or run a game that uses it. Removing Java from OS X is involved so if you have installed it the best thing to do is to disable it. See the link below for instructions on disabling it.
Click here for instructions for how to remove or disable Java from any machine.
Update 9/9/2012: Peter below asks why bother?