Actually, Java applets are a nice technology which could have been as ubiquitous as Flash, if only Sun didn't lose the PR and technology war with Microsoft.
Microsoft was pushing DirectX controls at a time, and leveraging IE market share against applets. I remember doing some benchmarks then: Java applet of 3 MB (which was large), loaded from local disk (to take network load times out of equation), took around 5 seconds to start in Opera. The same applet somehow took about 2 minutes to start in IE.
So, it wasn't that technology sucked; it wasn't that applets were slow because they were too big; they were slow because the dominant browser at the time deliberately made them slow. :)
I guess that JavaFX is Sun's attempt to revive a lot of ideas from applets, at a different time and in a different market.