There are a lot of things that can be done though. Facebook and Netflix [1] for instance are crawling the web for leaks and pastes, once they find one of their user's password they will force the user to change their password. Auth0 is a authentication-as-a-service and we offer this as a feature [2].
I have worked on this feature and several related features, my advice is don't ask for a password in your public website. If you think is easy, you are wrong, it is a lot of work to code it correctly but it is also a lot of work maintaining the system. Brute force protection, anomaly detection, detecting when your user password has been leak by a third party, etc. It is simpler to authenticate by using a third party like google, you just have to be careful about implementing oauth flows correctly.
DISCLAIMER: I work for Auth0.
1: http://www.dailymail.co.uk/sciencetech/article-3628950/Time-...
2: https://auth0.com/blog/announcing-password-breach-detection/