Applets are another example of a great idea, poorly implemented. While it's getting better, but there are still a few common problems associated with applets. Browser incompatabilities, differences in JREs, as well as the extra bandwidth and client-side muscle which it takes to run them.

Overall, I am not opposed in applets in web-design -- however, you pretty much always have to have backups for the places where Java isn't practical. Or risk alienating people on slow modem connections, Linux/Opera/Netscape 2.0 users, or anyone who turns their Java off.