I was wondering about making a "bitchain messenger" that allows you to send messages to others and then those messages are signed and encrypted into the bitchain? Sort of like how bitcoin sends coins - you'd be sending text messages (like twitter). Each message would cost 1 coin, but it could be a relatively cheap coin like LiteCoin - and when you send a coin, you also have a space to send a message. You'd have anonymous messaging and currency. So, for example you could order something and include your shipping address with your payment. Or perhaps just use it as a jabber replacement. Messages would only be delivered after 6 or so confirmations. You could for example place a bet by sending a coin (and your message would include the pay-to address so you could get paid if you won the bet). You could play chess online by sending the moves (ex: Rb3 Na1) and you couldn't take back moves or cheat.
In principle this is a very interesting idea. This would in effect be like P2P email, where the message gets encrypted and stored in the bitchain - call it a mailchain. Would be interesting for messages which need to act as proof under certain circumstances. E.g. legal contracts. Then the chain can act as a timestamp which cannot be falsified. It would be a decentralized notary.
Since the chain only has to be self-sufficient you could have a constant coinbase transaction per block which equals the amount of available bytes in a block. E.g. if you set the hard limit to 1MB. you allow the generation of 1M coins per block. Then a message costs exactly it's amount in bytes - otherwise a miner should reject the message.