At which point does it become illegal? Is sharing it with one or two people ok? I would think that even putting it in your public folder is not necessarily illegal: What if you don't share the link publicly (or only with one or two people)?
Services like Rapidshare thrive on those ambiguities. They let you upload any file and give you a link, only after this link really becomes public will they take down copyrighted content (which introduces a time delay).
I have actually never seen that happen with Dropbox links (which, I think, is the right strategy for them: It would be bad for their brand if they were to become "that piracy website"), so they must be doing something different.
We're not Big Media people, but what about other content creators? Especially musical collaborators...
Actually, it could be. Copyright means exactly that: the right to copy.
As I said, copyright law is quite complex and full of exceptions and clarifications.