This is what we are currently selling. I've no idea how it looks like, but it seems to work. Another group maintains it, not my business.
Another thing I've seen: http://www.gladinet.com
All those cost money, in some form. I always wanted to try Seafile, it has some interesting features (like client-side encryption). Recently, there was a bit of a fall-out between the developers in China and the people in Germany who sold support for it. It's a bit messy at the moment...
Go for http://www.gladinet.com/serviceprovider.html you wont look back. Setup your own server to host your clients cloud files. Use any external storage provider.. (You wont be keeping any data in your server) Set your own pricing, charge your clients directly.
I want an abstracted file system -- let the app worry about which actual account/service hosts each file.
In the last 24 hours, getting a little more creative and persistent, I've found two cloud storage managers which will do this:
Storage Made Easy and their "Virtual Cloud File System"
Gladinet and their feature purporting to "Unify file server structure from multi-site"
If I find more, or when I decide to commit to one of these, I'll update the post.
If you're on PC you can use SkyDrive, which offers 25 GB free storage. It doesn't have a native dropbox-like client, but the Gladinet desktop client will take care of it.
If you need more space, and don't mind a bit more of a techy setup, try Gladinet (the free client is fine) and Windows SkyDrive (25GB and free). I wrote a short blog about something nifty you can do with the both of them.
I use a separate SkyDrive account as a cloud backup of the most important documents and pictures on my computer! Both are free.