Here is a link to a file in my public Dropbox folder: http://dl.dropbox.com/u/4073000/Dropbox.txt
I have never actually seen anyone share Dropbox links to pirated content. I don’t know why that is (pirates seem to use all other services which allow you to upload files) but as far as I can see, Dropbox has no big problems with piracy.
I think that hosters like Rapidshare have an upload quota but no bandwidth limit. Bandwidth is limited for downloaders, not uploaders. (It’s impossible to download much without paying but an uploaded file will not become inaccessible because too many people download it.)
Rapidshare obviously makes money with piracy so they cleverly encourage it without overstepping legal boundaries. Dropbox is a very different company, I don’t think it would be good for them to be seen as a tool used be pirates which is why the cleverly discourage it.
You will only upload, post, submit or otherwise transmit data and/or files: (i) that you have the lawful right to use, copy, distribute, transmit, or display; or (ii) that does not infringe the intellectual property rights or violate the privacy rights of any third party. Dropbox has adopted and implemented a policy that permits the deletion of files that violate this policy, and that permits the termination in appropriate circumstances of the accounts of users who repeatedly infringe or are believed to be or are charged with repeatedly infringing the rights of copyright holders.
As a current dropbox user, I'm a bit concerned about this functionality (since by default public means public but unlisted, it can still be shared). Hope these guys did a bit of homework here.