Are there any non-monetary uses for the blockchain, or the Bitcoin protocol generally? After reading "Have there been attempts at a Bitcoin-powered general purpose database?", I'm wondering if any other uses have been made (or proposed) of the blockchain and Bitcoin protocol that aren't solely about financial transactions (and directly related activities like mining)?

(Perhaps something similar to Bitmessage, but using Bitcoin itself rather than simply taking inspiration from it.)
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