Yahoo allows for mobile-device-as-token to replace email passwords

Yahoo Mail Now Accessible Without Password (Latinos Post)

"You log into your Yahoo account using your normal passwords. In the security settings, you turn on on-demand passwords and register your phone. Next time you try to login, the password field is replaced by a button that says 'send my password,' and the company texts a four-character password to your phone."

There are, however, critics of this approach. See Yahoo’s attempt to kill off passwords raises security concerns at Computer Weekly.