The question seems to focus on exact match hashes, which we understand better than nearest-neighbor approaches, and are indeed worthwhile, especially if people can share tags and other metadata that way.
As @rjmunro notes, hash-based searching is a popular idea in the P2P world, and Bitzi did pretty much this, though they have shut down and their Bitpedia (Digital Media Encyclopedia) isn't hosted there any more, though some of it at least is still available at Archive.org.
Bitzi also produced software like Bitcollider (SourceForge.net),
and the Magnet URI scheme, which allows for specifying a file by hash and is thus a content-based identifier. Various applications support searching at various databases via Magnet URIs as described at that Wikipedia page.
The same idea is popular in the password-cracking scene - see e.g. findmyhash - Python script to crack hashes using online services etc.
Going a step further, I think it would be great if there were databases and online repositories identifying content by hash and providing tags and other metadata about the content from various perspectives. Then I could leave my music collection in its pristine state (no wasted backup space and time), but still tag them myself and add other metadata, via external tag databases. If my applications knew how to grab the tags, it would seem much better than the current system where we modify and copy around big files just to move tags from e.g. my desktop to my phone.
See a related idea at Metadata Independent Hashing for Media Identification & P2P Transfer Optimisation (pdf).