After some applets wouldn't run in either Chrome or Firefox on my Fedora 18 system, it was time for some investigation.
First I tried installing Oracle Java as some applets might be requiring it explicitely.
Oracle Java
Download Java from
here. Follow the instructions for installing, from
here.
Then, open "about:plugins" in your browser and check if the Java plugin is displayed there.
Verify Java installation
here. Test applet support
here or on
JavaTester.
Remove old versions, as specified
here.
While I first installed 32-bit version of Java, as suggested on Oracle's site, this is not correct. The proper version to install, even for applet support, is 64-bit, if on 64-bit system. After installing 64-bit version and setting it to be the active one, using 'alternatives', applets worked in both browsers!