Here is a simple class that allows you to transfer files via WebDAV.
Inside it uses: CFNetwork for HTTP/HTTPS connections. Streams for reading and writing files. NSXMLParser for parsing WebDAV responses.
Known Issues and Future plans: At the moment it doesn't provide anything unrelated to file transferring. It doesn't support resuming upload/download and timeout handling yet, but I'm working on this. No documentation yet, and not many comments in the code. However, there is a simple example for the iPhone platform.