Java Applets died not because of the concept of an applet, but because the JRE plugin for web browsers was abyssmal.
In fact, Flash proved that there is a role for in-line interactive content.
JavaFX is a new way of programming rich internet applications - essentially equivalent to Java applets or Flash content. The new JRE runtime (1.6.0_10, aka "Update 10") includes lots of features that make running Java in the context of a browser much more palatable.
JavaFX != Java Desktop. The two are quite different, and each have a place in a developer's toolbox.