Are there any non-monetary uses for the blockchain, or the Bitcoin protocol generally?
Proof of Existence is a good example of innovative use of Bitcoin network. The idea is as follows: 


  use our service to anonymously and securely store an online distributed proof of existence for any document. Your documents are NOT stored in our database or in the Bitcoin blockchain, so you don't have to worry about your data being accessed by others.


More details:
http://www.proofofexistence.com/about