One of my clients recently had a problem playing facebook games using Firefox. The funny thing is that only some games had problems, while others were fine. Inconsistencies like this make troubleshooting a problem difficult.
But while going through the normal steps to correct the problem, I came across a small note the other day on the Java website that mentioned a compatibility problem with the latest version of Java (6 update 18) and Firefox (version 3.6). It's a tricky issue, but in short, before upgrading to the latest version of Firefox, you have to have an older version of JAVA on the computer.
People like me, who always uninstall older versions of software before installing newer versions, are the ones who primarily seeing this problem.
Without going into too much technical mumojumbo, if you're having trouble playing games on Facebook or other JAVA based games, you might want to try these steps to resolve the problem.