I think that it is safe. Personally, I use
Dropbox for storing files online because the first 2GB are free and you can sync it on any other computer/server as well so it is handy for backups too.
Another service that I've used an would recommend is
Egnyte. It's also really safe but quite expensive compared to Dropbox ($29.99/mo).
So as a conclusin I think that online file storage servers are still safe, but it depends on which service you use (IE. Dropbox or Mediafire).
Regards,
ford