Tools; Internet Options; Programs; Manage Add-Ons; insure Java ActiveX controls are all enabled.
FYI: This path showed more Java options than going to Tools; Manage Add-Ons which never gave me the option of enabling an activeX control for Java Platform SE Binary. Once I activated that, the applets began showing and working. All the other suggestions regarding setting the options under advanced (use java applet) and security / custom re: allow java scripts did NOT correct the problem until I found this way to enable the activeX control.
Hope this helps others who have been searching as long as I to find a way to make this work. the clue was that Firefox and Chrome worked the java applets fine but IE7 didn't.
Thanks so much for posting this!!! Thanks to you I was able to fix my problem in no time.
Java was working for me in Firefox but not in IE7 and when I went to the Java site it didn't detect Java on my system at all. I re-downloaded it and it still wasn't working in IE7... until I enabled one of the Java ActiveX controls as per your instructions.