Does ruby run yet on R-Pi?
If so then a cmdline tool like S3Sync would work with GreenQloud's QloudStorage. We would be happy to setup a playground account (Storage Qloud is an S3 clone so all the tools work with it).
DropBox is a sync tool like s3sync so you are always consuming local storage which isn't the best solution. Dropbox would work if Android could be run on R-Pi as would countless other apps.
Another cool DropBox like solution is OxygenCloud which has the cool feature of NOT copying the file to local storage unless you access it but they only run on mainstream OS's still.
So the first qualifying question really is sync or mounted storage? There are lots of webdav clients and servers (that mostly suck) and then there are "userland" network storage filesystems. Most of them are "virtualized" through Fuse.
If anyone could get Fuse built on R-Pi then that opens loads of options. Then again it's probably easier to just get NFS or Samba running...