Saving of new passwords
Offer to save new logins or add to existing login when no passwords can be found in database.
Corne Beerse commented
For some browsers this is already available: Tools -> Options -> AutoFill -> Passwords. Here just select 'ask'.
Next: if you are at a page to give the login, just ask for it. If there is no suitable login, it provides a way to give the info, sets it to the page and saves it.