Is there any good browser based WebDAV client? If not, is it possible to make one?
Depends on what you expect the client to do, and whether you're looking for a cross-browser "web application", or a browser extension.
The main issue with doing this in a "web application" (as opposed to a browser extension) is (1) the lack of binary data support in Javascript, and (2) the lack of access to the local file system (which of course is a security feature).