I think Java applets were overshadowed by Flash and ActionScript (pun unintended), being much easier to use for what Java Applets were being used at the time (animations + stateful applications).
Flash’s success in this respect in turn owes to its much smaller file sizes, as well as benefiting from the Sun vs. Microsoft suit that resulted in Microsoft removing the MSJVM from Internet Explorer, at a time of Netscape’s demise and IE’s heavy dominance.