Well, technically DVCSes like git use "blockchain" (the repo, logically, is pretty much a chain of blocks that incorporate the hash of the previous blocks - just tree instead of linear dependency).
So we are already successfully using blockchain for decades just not as... currency provider.
Forward secure sealing (used in logging) also have similar idea
What makes it a block chain instead of a tree is that there's a way to form consensus on which block is the next in the chain.
What makes it different than database logging is that the consensus method is distributed and decentralized, and anyone can participate.