I just activated the Google app authentication on my Google account. First attempt on login failed which was a bit annoying, but second one was already successful (even Google might not get things right the first time it seems ;-).
Now logging into Gmail on my laptop's browser goes like this; I type in my email address and click submit. I receive a pop-up on my phone asking for authentication. I unlock my phone with a fingerprint and click "OK" on the Google app and punch in my fingerprint as an additional security measure. Now I'm in without needing to type in my 22 character password sentence including capital and normal letters, numbers and special character. WHICH IS PRETTY AWESOME! And it just gets better on my mobile's browser, not needing to type in my lengthy password when using services linked with Google account! For occasions when I don't have my mobile at hand, I can still choose to login with my password.
I'm not using the mobile app login for two factor authentication, but there might be actions or sites that where the service provider would require me to also submit my password in addition to my mobile authentication.
What's also really cool, you can provide this kind of login experience easily to your own customers. We have implemented for example a mobile app based login with an open source authentication server called Gluu. There's also an open source mobile auth SDK that you can integrate with your own apps, or Gluu also has a separate licensable authentication app called Super Gluu.
So stop bothering customers with passwords and make their online experience better!