No, JavaFX is not a replacement for applets. In fact, the idea is that you write applets using JavaFX for things like what you can do with Adobe Flash or Microsoft Silverlight.
Therefore, instead of replacing applets, it was expected that JavaFX could again make applets popular.
edit (08/15/2009) my answer is above 10 years - everything has changed. Applets are no longer supported; Oracle does not provide a Java browser plug-in that can run applets with current versions of Java. Do not write code that uses applets anymore.