IMO, sites should generate a >20 character random base64 password as a form prefill on the registration form, which hopefully would cause browsers to remember it (don't actually let the user change this). Provide "show password" and "copy password" options for those who need to write it down for use on other machines or want to export it to a non-browser based password manager or sync tool. Encourage users to have a master password for the browser password storage.

Also, many sites should have an easy email based login.