ESecureDOX provides just about exactly what you're looking for. It's a cloud storage system run by a digital certificate authority, which means that each user is assigned a free digital certificate and PKI key set when they sign up, and each document is automatically encrypted by the storage system when you upload it to the cloud. Your document can only be accessed by your user account because of the technology behind the individual encryption (asymmetric PKI), so that the encryption code for each account would have to be separately compromised in order for any data to be compromised. And that's unlikely: the encryption that it uses would take 20 mainframe computers 20 years to brute force, according to NSA estimates. This opposed to something like dropbox, which only uses SSL encryption. What that means is that if someone were to gain access to the blanket encryption that dropbox uses, every file on the system would be compromised.
As far as your concerns about sharing a document, when you share a document through ESecureDOX, only the single document is decrypted by the system, and that's done in a way that whomever receives your document is unable to edit it. This allows the sharing of documents without the concern that they'll be tampered with, and without allowing access to any files besides the one you want to share.
I apologize if this is overly dumbed down, but I just wanted to make sure that the advantages of the system were very clear. From the user interface ESecureDOX seems almost identical to already present cloud storage systems, but that's only because the PKI encryption and decryption happen behind the scenes. It can do that because the company that runs it is able to issue its own root certificates and integrate them into their storage solution without the user needing any technical knowledge of PKI or requiring them to keep track of their own keys.
Edit: for full disclosure, I do work in marketing for the company that runs ESecureDOX, Image-X Enterprises. But I haven't misrepresented how the service works in any way, and I do believe in its advantages regardless of my affiliation with the product.