Another option, apart from Applets, is Java Web Start:
Java Web Start software provides the power to launch full-featured
applications with a single click. Users can download and launch
applications, such as a complete spreadsheet program or an Internet
chat client, without going through lengthy installation procedures.
With Java Web Start software, users can launch a Java application by
clicking a link in a web page. The link points to a Java Network
Launch Protocol (JNLP) file, which instructs Java Web Start software
to download, cache, and run the application.
If you are planning to do something very CPU consuming is better to use Java Web Start. But if you need some JavaScript And Java interaction it would be better to use the old Applets.
If you are worried about browsers blocking or not supporting Java Applets, then Java Web Start is again a better option.
The following links may be of interest to you: