What is Dropbox?
If you haven't heard of Dropbox yet, I strongly encourage you to go check out their website immediately. Essentially, Dropbox transforms a normal folder on your computer into one that syncs automatically online. If you install Dropbox on multiple computers, all those computers will share the folder and you'll have access to everything in that folder anywhere. It can even be used to take your passwords with you.
From a programmer's point of view, it behaves like a folder under version control that automatically syncs any time something new is added or modified. It takes care of merging and conflicts without ever bothering you (in case of conflicts, it just shows both files and renames one of them appropriately).
Dropbox doesn't currently offer a self-hosted solution and I think there's an opportunity here for someone to fill a small part of the market. Companies could offer accounts to their employees and/or share folders among all the employees. An open-source solution would certainly be doable, there's no need for a fancy web interface (although it's pretty useful), the core of the application isn't too big. Someone even managed to get something running that offers the basic functionnalities of Dropbox.