Here's a list of some useful and creative Java applets on the Web. Please add descriptions (with URL) of other applets that merit inclusion.
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A complete JavaLanguage implementation of a SecureShell client in an applet. This is useful because if you are on a machine where you can't or don't want to install software, you can still fire up a Java-enabled WebBrowser and get to any ssh-ready server you want. http://www.mindbright.se/products/mindterm/
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EuclidOfAlexandria's Elements in Java: you can manipulate the points in the diagrams, and see what effect it has. Not necessarily useful (unless you happen to be studying Euclid), but still a decidedly good use of Java. http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
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While not really "Useful", probably the most popular Java Applets are at yahoo games.
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WikiComposer. Also has the advantage of being a wiki (to the extent possible with music)
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Emulation World Network - multiplayer NES emulator http://www.emuwn.com