Notaries are used to authenticate documents, providing additional weight that they mean what they say they do (and are between the people they’re supposedly between). I had this idea back during the dot-com era, and the core of it is that you build a company who’s primary purpose is to authenticate that documents were created at specific times (and to a lesser degree, by specific people).
This could, in theory, be used for legal documents and whatnot, but in the early stages might find usages such as professionals who are required by law to keep notes (such as psychologists, medical doctors, and lawyers I believe). Having documents provided with a time stamp authentication would prove that the professional hasn’t altered the document after a problem occurred.
To set up this sort of company, you’d need to focus on establishing your site as very accurately recording time and identity (or being very precise about what you’re verifying as “the identity” it could be that you’re authenticating based on an e-mail address or phone number). Security would be a major issue, and great lengths would need to be taken to show that it would be very difficult for someone to forge a document in your system. You would also need to convince users that your system will continue to exists indefinitely. If there’s any doubts about your ability to stay in business it would severely undermine you. Obviously you’d want to have the actual data encrypted (so documents are only ever seen if the authors release them), and multiple redundancy (at multiple locations) so data is never lost.
This might work as simply as a user uploads a document along with an e-mail address and/or a phone number (with a password). The system automatically sends out a confirmation e-mail (which they click the authentication link and enter the password). The phone number would be called and the password requested. After this, the system would verify that the document was submitted AT THAT TIME by someone who had access to THAT e-mail or phone-number. If the system had a login and password as well this wouldn’t PERFECTLY prove their identify (there would be ways to defeat the security of each identifier), but it would take A LOT of work to beat all three (and in my opinion would be at least as secure as notaries – faking ID would be easier than defeating this type of system).
Documents could be released by a code which, after the author chose to release it, could be given to anyone who could then see the document on the site and verify its contents and date of creation. Options to selectively release parts of documents would also be possible. Extra features like automatically releasing the document to specific e-mail addresses (or mailing hard copies to specific addresses) at some point in the future or using a dead man switch could be optionally offered.
As the system became more accepted, more usages could be built on top of it (and eventually it could become a platform offering authentication of documents in a legally neutral way – not tied to any particular country or legal system). Perhaps people could form a contract by uploading identical copies of an electronic document and both authenticating their copies. The system could tie them together and let both parties know that the other has authenticated it.
In terms of a business model, I’d let users store small documents for free (and pay a fee to store larger documents), and pay a modest fee to retrieve/authenticate them. This would be billed as getting all the benefits, and only having to pay it there’s a problem (and you need to produce the authenticated document).