Java Applet seems out of favor these days. Flash is so dominant with penetration 99% for Flash 9 and 95% for Flash 10 as of December 2009 and it seems capable of doing everything that applet can do.

My teacher/boss/other misguided person insists that I embed a component in the web page; can I use an applet then?
Sure... we just recommend that you use a Flash applet instead of a Java applet. Flash support for embedded content is much more uniform than Java. The Flash run-time is more suitable for the kinds of things that you can do with a browser and web server interaction. They are more limited than Java Web Start but they are better designed for browser-based applications. - from Java Channel on applet

Though we can use Java Web Start (JWS) instead, I am not sure of its future, either. Startup time is relatively big for the world of web where even 1 second is considered forever. There is also JavaFX option which some have been speculating that it will compete with Adobe Flash Player. Compared with matured Flash technology, it seems it is still in its infancy at 3 and has not taken off yet. Compare the number of pages from Google when I typed in following keywords: Adobe Flash = 237.0 million, siverlight = 15.8, Applet = 8.5, JavaFX = 1.4, Java Web Start = 0.5 as of Feb 2010.

Whatever the future of Java's client side technology would look like, I think it's worth trying or investigating to get the best of it.

My gut feeling is that the time will come. Who is the star player in the world of web now? It's the web designer. It's web designers' heaven. I do not have any intention of insulting them. They are making our web more fancy and good looking. Sometimes they even make it dynamic. Not just dynamic but also artistically appealing unlike a lot of ugly looking Applet produced by scientists or by engineers.

But when web pages need more computing power, we may want to tap the very power from the language we use. HTML? No. Slow Javascript, though it's the only official script in HTML5? No. Flash? Maybe, if the web requires not that much computing power.

When we are complaining about the slowness in booting Java Applet or Web Start, it may well be the same situation we are using gas truck full of gasoline to fill our lawn mower. Who knows, in the coming cloud computing era, we will be appreciating full fledged power of Java Lang with some 3D Graphics like OpenGL. Nobody is going to complain about even for 1-minute loading time when they want to run huge Java WebApps not applets. It will be much better if future web does not require Plugin for Java.

But at this time, I do not hava any good Applet examples for this page. Applet was not my area of interest at all. But a couple of years ago, I briefly worked on Java Web Start just for experimental purpose. I made a simple picture with OpenGL graphics with Java (JOGL). You can rotate/zoom/pan the picture.

• rotate: left mouse button
• pan: middle(wheel) mouse button
• zoom: right mouse button

Java Web Start sample Java with OpenGL

Regarding the real examples of javaws, NASA World Wind has the most extensive list of demos with quality. They are using JOGL with Java Web Start.

Table. Java Applet vs. Java Web Start (JWS)

Factors	Java Applet	Java Web Start
Offline support: Run without browser?	No, applets are embedded and should be started via browser. It is a small program that is intended not to be run on its own, but rather to be embedded inside another application	Yes, JWS allows applications to be launched independently of a Web browser. The application can also be launched through desktop shortcuts, making launching the Web-deployed application similar to launching a native application.
Caching: Must wait for download every time?	Applets will be always loaded from the scratch. So, applets take roughly the same time to download on first use and each subsequent use.	Applications launched with Java Web Start are cached locally. Thus, an already-downloaded application is launched on par with a traditionally installed application and will load faster on subsequent uses due to caching.
Security viewpoint	Applet are restricted by the sandbox environment, which provides a powerful defense against rogue applications.	Java Web Start provides a secure API that enables an application to import and export files from the local disk under the user's control. The API includes dialog boxes for operations such as saving a file and opening a file that are actually rendered by Java Web Start, and not by the application itself.
Nutshell	Lightweight use	Heavyweight use

This page in still underconstruction. In the mean time you can have the article below.

Another way to provide Web animation is through the universal, network-oriented programming languages known as Java. With Java, programmers can create applications that users download off the Internet. Java-enabled browsers use a virtual machine, a piece of software that recognizes the Java language and translates it for the user's computer system (Windows, MacOS, Unix). The virtual machine is basically a kind of plug-in, and it must be installed with your browser.
Java Web content is generally created as programs called applets. Applets aren't complete software applications -- they work only in conjunction with a browser. There are all sorts of things Web designers do with applets, and one of the most popular applications is animation. The main advantages of Java are that it works on all operating systems and it is very flexible. You can create an animation program that draws simple vector shapes for the individual frames, or one that uses bitmap images. Java is particularly suited for creating interactive animations and combining animation with other Web page elements. - from howstuffworks

My stuff is coming soon.