Dropbox is actually pretty invasive. They save space and bandwidth by recognizing media files that other people have stored and just copying internally instead of uploading from your computer.
Not really surprising
Specifically I recall a story that pirates were using their api to just upload the hash and basically use it as a file transfer service. They had to start requesting random chunks of files to make sure you actually had the file you were trying to sync.
Edit - I found a link: http://www.wired.co.uk/article/dropbox-dmca-position
The file uploaded in an instant, lending a lot of credibility to the theory that the software hashes a file and looks for the same hash in a central database, and if there's a match doesn't bother to upload the file but simply adds a pointer to it.