I run the IT shop for a non-profit, which has just started to expand globally. I've been brought in to help ease the pain. We've got nearly everything web-based, except for the damn "shared drive". We just can't afford to set up a permanent VPN connection to all of our new offices (and all of the road-warriors)... nor do I want to.
I'm testing Alfresco now (http://www.alfresco.com/), which is basically an open-source SharePoint. It's web-based, with file versioning (and other bells and whistles) but best of all it emulates a SMB/CIFS share, so the transition is easy for the main office. Hopefully it works well and I can implement it.
But as an avid dropbox user, even this huge leap feels so old-school. It'd be great if remote users could "subscribe" to some of the folders, so they could work with files more quickly and offline. It's the future.
An open-source DropBox allows for corporate implementations ("my data stays on my servers" types), and also permits tie-ins to other open-source projects (like Alfresco). The service won't be as bullet-proof and smooth, but the mashups will be interesting.
Edit: DropBox should really offer corporate solutions. We're poor, and I think we'd spend money if I could sync our shared folders out to their servers, and let all my users access it from their beautiful web interface. That alone (without the client features) would be worth it.