Question: I would like to list the directory that my current website will be in as a browsable tree (similar to the way a web browser lists a directory if there are no index files present) - basically, an FTP listing. However, I can't use PHP because the server I'm developing for does not support PHP (or any similar tools as far as I'm aware). I do have access to JQuery, and Java and Flash applets, though.

My question is, first of all, is that even possible? I know I can make a link that will make the browser list the directory for me, but I want this embedded within my own website (i.e. inside a div). I would prefer doing it all with just JQuery/Javascript. I'm also fairy fluent in Java, but I don't know if I can list directories in an unsigned applet.

Answer: 
I don't understand your problem completely, I see only one possible solution without a server side language.

Include tree like structure for all directory components(path) links (native htmls) in index.html and apply some basic jquery animation to feel like tree structure.
Jquery / javascript are client side languages, you must have something on your server.  

Perhaps if you'll have a WebService on your server, you can call it with jquery and format it in your html.