In Australia we can login to Internet banking and send money to another account with any bank in Australia free of charge and usually within 2 business days.
The user experience for person to person transfers varies and is usually poor.
Electronic transfers (ACH) only take a couple of days though, and for things like payroll, once the accounts are set up it all works fine. They also work pretty well for making payments to businesses and what not.
Is something like this not possible in the US?