As far I know, the Bitcoin blockchain is pretty much the only data structure that is both global and tamper-proof.
global - There is one global instance of the blockchain (up to forks ... which are then resolved). tamper-proof - If a block enters the blockchain, after 6+ confirmations this block can't feasibly be faked or altered.
A Bitcoin-powered database would be an API over the blockchain, that would expose a subset of the usual CRUD database operations. In fact, it would be an append-only data structure, because nothing can ever be really deleted from the blockchain - so only CREATE and READ operations will be implemented. Object Versioning will be used to emulate updates and deletions.
Have there been previous attempts to create such a database? I have seen the MerkleWeb proposal, but I haven't really understood it, so I'm not sure if it answers my question.