As a small team of developers/friends, we had created a simple intranet platform (years ago) to share ideas, files (and keep backups), manage our e-mails, etc.
Few days ago, after discussing "how awesome it would be to use the file sharing module of it from a Dropbox-like application", I started searching for any open source tools that can do the job.
As expected, yes, there is open source for everything and found very nice resources that can help us accomplish the project with almost no (or few) coding.
Considering you may use them in your own projects/platforms or have an idea of building a file storage and sharing application, here is a complete list of open source Dropbox alternatives (that are updated regularly):
SparkleShare (Mac & Linux)
This is a file sharing and collaboration tool which allows you to instantly synchronize with any Git repository (SFTP is on the way).
It can connect to any number of hosts + allows you to follow and add/remove files into any number of projects.
Growl notifications let you know when a change by a team member.
Syncany (Windows & Linux)
Syncany is a very promising and open source file sharing + storage application which is still under heavy development.
It can use almost any type of storage including local folders, FTP, Amazon S3, Google Storage, IMAP and more.
The data is encrypted locally which is nice for the security of sensitive information and has support for versioning.
Read more: WebResources depot