WebDAV is an extension to HTTP, and is growing more and more popular as a standard for file-sharing.
WebDAV (shorthand for Web-based Distributed Authoring and Versioning) is an extension of the standard HTTP protocol designed to make the web into a read/write medium, instead of the basically read-only medium that exists today. The theory is that directories and files can be shared as both readable and writable objects over the web. RFCs 2518 and 3253 describe the WebDAV/DeltaV extensions to HTTP, and are available (along with a lot of other useful information) at http://www.webdav.org/.
Saving files directly to a WebDAV share (i.e. from within an application, such as Word, Excel or Internet Explorer does not work reliably. For best results, save the file to your computer first and then upload it to your site.
A number of operating system file browsers are already able to mount networked directories using WebDAV. On Win32, the Windows Explorer can browse what it calls Web Folders (which are just WebDAV-ready network locations) as if they were regular shared folders. Mac OS X also has this capability, as do the Nautilus and Konqueror browsers (under GNOME and KDE, respectively).
Also see http://en.wikipedia.org/wiki/WebDAV for further information.