Well with Mailbox, it's getting close!
Cloud storage provides virtually unlimited free storage. Copy, Dropbox, Google Drive, Box, SugarSync, Evernote, Bitcasa...the list goes on and on. All offer a free option and a paid option, but if you're willing to spread your files around and make use of referral links (see bottom of my home page for links to cloud staorage that will get you more free cloud storage), you can have virtually unlimited free storage.
Cloud provides you with web-based access to your files, basically anytime anywhere you have internet access. And you can download any of your files for local edits and backups if you want.
Cloud provides more security and redundant backups than you ever could provide for your own local files. Most offer georedundant storage sites (if an earth quake takes out the west coast, your files are still in good hands), and HIPAA and FERPA compliance. CIPA compliance has been a challenge for cloud, as it has for so many other web-based services. Official user agreements insist users must be 13, but many are under 13, we assume with parent permission. Many expect CIPA to be updated soon to reflect the in-the-cloud reality many web-based services are experiencing.
Mailbox changes that...