Yes, recurring payments and subscriptions is a frequently-requested feature.  It needs a new BIP.  Here is an outline:

The situation is somewhat analogous to HTML5 local storage.  The remote (merchant) wants to initiate a persistent behavior.  This is bitcoin, so we have a "push" model for payment, and the user has complete control.  The merchant can, at most, send a "subscription request."  The user is responsible for making on-time payments after that point.

Centralized services like coinbase.com or blockchain.info will have an easy time of it.  An automated program on their backend, sending payments as needed, is easy and direct.

More inventive services might employ multisig transactions, generating and signing one signature of a TX, then sending that TX to the human for further signing and publishing.  A few competing vendors could offer bots that provide this signing service.

Decentralized, standalone wallet clients will be somewhat troublesome.  We can store a local subscription request, and send recurring payments...  if the wallet app is running.  If not, the user will be missing payments, that perhaps they intended to make (rent!).

Each of these solutions can be cancelled at any time by the user.  As such, a courtesy "subscription cancelled" message sent to the merchant is recommended.  User controls the usage of their money at all times, the way things should be.

And finally, you do not want to make it /too easy/ to send money over and over again.  From a human-interface perspective, a textual reminder to send money might be preferred over actual recurring payment automation: reminder email + manual spend inserts a bit of additional human thought and review into the process, with all that entails.

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Jeff Garzik
Bitcoin core developer and open source evangelist
BitPay, Inc.      https://bitpay.com/