JavaFX is now out, and there are promises that Swing will improve along with JavaFX. Gone will be the days of ugly default UI, and at long last we can create engaging applications that are comparable to Flash, Air, and Silverlight in terms of quality.
Will this mean that Java Applets that hail from 1990's are dead and not worth going back to?
Same with Java Desktop: What will be compelling for us Java Developers to use it rather than JavaFX?
In my opinion Java Applets have been dead for years. I wrote some in the late 90s - a Tetris game during an internship to demonstrate on a 40MHz ARM Acorn Set Top Box for example. Of course I bet there are some casual game sites that have tonnes of them still, and thus it will remain supported, but active development will/has dropped off.
Java Web Start is a handy technology in my opinion. That will still work with JavaFX, it's just another library for that system.
JavaFX will give Java opportunities beyond technical tools (like SQL Developer), in-house business applications and server applications (where it excels). I think it's one of those libraries that is worth learning for any Java developer, if they can get the time. There's no arguing that user interface libraries for Java have been sorely lacking, or overly complex, for many a year.
However there's a lot of competition out there, and it is very new (which means the development tool support is very raw, compared to Flash and Silverlight). Also people don't like downloading massive runtime environments, although broadband makes it less painful than 5 years ago for many!
I think this discussion is somewhat misleading. I an no fan of applet technology either (and I have been underwhelmed by JavaFX). But the point that this thread is missing is that, unless I am mistaken, JavaFX is built on top of applet technology. They are not competing or mutually exclusive. See these articles here and here.
It could be that the confusion is somewhat intentional on Sun's part as they do not want JavaFX and applets to be mentioned in the same sentence, since Applets had so many problems.