I have never used OS9 or OSX, but according to the WebDAV projects page OSX definately has support for WebDAV. Also Win9x and up also support it (earlier version may need to install the 'Web Folders' update on Windows Update).

WebDAV is an open standard, and hence you should get excellent cross platform interoperability. At it's most simple level, you could call it FTP over the HTTP protocol (which is pretty much what you were after). But it allows much more than that, especially with the power of Apache driving it.