Since AJAX has become very popular- with its ability to connect to server side resources from the client browser-- will or has the Javaapplet follow suit? Maybe it has already, however I cannot find anything that suggests you can now access server side resources like a MySQL database.
Applets have always been able to do this. Any kind of TCP/IP network connection is possible: JDBC, HTTP, raw sockets etc. The only restriction is that it had to be to the same host where the applet was served from. But that's the case for AJAX as well.