Citibank and Chase both have money transfer services via email. QuickPay and PopMoney, I believe. I have used both of them and they work. The sender needs to have an account with the originating bank, either Chase or Citi but the recipient can have an account anywhere with a routing number and account number. The bank facilitating the transfer will ask for ACH access to your receiving account and place some small transfers into your account. When you see those transfers they are like activation codes which you then use to validate that you are the owner of that account.

This certainly works in one off situations but I would love to see Citi or Chase productize this via an API for authorized merchants, etc.