@Ignacio: Java could achieve some features easily, but I don't know about 'sleeping in the tray' (that sounds a lot like Windows) or how it would deal with each OS file management for syncing files.
My main point is that programming for the client (and maintaining the apps on the client side) is a lot harder when you exit the browser. The more we can achieve with the browser, the best.
Then, for better integration with client devices, I would go the 'standard-web-services' way, providing services and interfaces that client apps and devices could sync with (WebDAV, LDAP, iCal, etc.).
@Max: Great initiative!