On June 18, 2013, Oracle released Java 7 update 25 (1.7.0_25), which introduced an incompatibility that prevents PhET simulations from launching when using either the “Run Now” button on the website or the PhET Offline Website installer.
Oracle has fixed the problem and the fix should be available in the next version of Java (although this new version may not be released for some time).
Until this problem has been resolved, the best work-around for users experiencing this issue is to “Download” local copies of the simulations. When you press the “Download” button on a sim page, a “.jar” file will be downloaded. You can then double click the “.jar” file to run the sim locally. (Please note: on a Mac, you will have to right-click the “.jar” file and select “Open.”)