Passwords get discussed a lot on this site, and there's quite a lot for both users and sites to do, to stay in line with "best practice".
Web sites need a password strength policy, account lockout policy, and secure password storage with a slow, salted hash. Some of these requirements have usability impacts, denial of service risks, and other drawbacks. And it's generally not possible for users to tell whether a site actually does all this (hence plaintextoffenders.com).
Users are supposed to pick a strong password that is unique to every site, change it regularly, and never write it down. And carefully verify the identity of the site every time you enter your password. I don't think anyone actually follows this, but it is the supposed "best practice".
In enterprise environments there's usually a pretty comprehensive single sign-on system, which helps massively, as users only need one good work password. And with just one authentication to protect, using multi-factor is more practical. But on the web we do not have single sign-on; every attempt from Passport, through SAML, OpenID and OAuth has failed to gain a critical mass.
But there is a technology that presents to users just like single sign-on, and that is a password manager with browser integration. Most of these can be told to generate a unique, strong password for every site, and rotate it periodically. This keeps you safe even in the event that a particular web site is not following best practice. And the browser integration ties a password to a particular domain, making phishing all but impossible To be fair, there are risks with password managers "putting all your eggs in one basket" and they are particularly vulnerable to malware, which is the greatest threat at present.
But if we look at the technology available to us, it's pretty clear that the current advice is barking up the wrong tree. We should be telling users to use a password manager, not remember loads of complex passwords. And sites could simply store an unsalted fast hash of the password, forget password strength rules and account lockouts.