As it stands, the only way to receive updates is to poll for changes. This is a kludge at best (and takes away from the magic in a significant way in practice) and completely unrealistic at scale. That is, if I have a million users and I want to update every 15 seconds, Dropbox is going to (rightfully) shut my IP down.
If developers could define WebHooks to receive events, that'd be a great start. I'd happily pay for that.
If developers could subscribe to a WebSockets or event XMPP notification stream of updates, that'd be freaking amazing. I'd stand in line to pay for that. And that's when you'd see an explosion of applications (web, mobile and desktop) implementing Dropbox as their filesystem.
We've been asking nicely for years. If there's anyone here with pull or influence at Dropbox, please give us devs some real-time love. Otherwise, please add your voice to the choir: