99% of sites require your email to set up an account, even ones that allow Facebook or Twitter for logging in. So why have any password at all? For that matter why bother with Facebook or Twitter?
To log in, enter your email address. The site sends an email. Check your mail. Click on the link. On clickthrough, set a cookie. Whenever there isn’t a cookie, go through the process of sending an email and clicking on the link again.