Discuss: When is it appropriate to use applets?

Last night my wife was enrolling in her university’s health insurance plan.  The insurance company’s website committed one of my biggest web development pet peeves: using a Java applet for a navigation menu.  This brings up my question: when is it appropriate to use a Java applet on your web site?  I’d appreciate your responses in the comments thread.

(As a side note, it was also very poorly implemented.  I got an error saying that I needed to make sure Java was installed for Internet Explorer on my version of Windows.  We were using Safari on the Mac!!)

Ted C. Howard @ted