Check your privacy settings to see what is checked.

In older versions of firefox I could check "Do not save passwords." In this version all I have been able to find is under Options>Privacy & Security a checkbox that says "Ask to save logins and passwords for websites." I don't see anyplace to say "Do not save logins and passwords." I don't want to uncheck "Ask to save logins and passwords for websites" and then end up making firefox by default save all passwords without asking. How do I assure no passwords will be saved? (And I wonder why this option--Don't save passwords--isn't straightforward on the browser privacy options page?).

Can you show a screenshot of that setting?

Make sure you do not run Firefox in permanent Private Browsing mode (Always use Private Browsing mode; Never Remember History).

• https://support.mozilla.org/en-US/kb/private-browsing-use-firefox-without-history

• Options/Preferences -> Privacy & Security
  Firefox will: "Use custom settings for history"
• remove checkmark: [ ] "Always use Private Browsing mode"

When I encountered the problem I had already unchecked "Always use private browsing mode". And, I had already set it to "Use custom settings for history". However, when I read the information on permanent private browsing, it sounds like that is one way to keep firefox from saving passwords. Is that correct? If that's the only way, I can do that for now. I'll have to consider other browsers because passwords are pretty serious to save; I don't mind other stuff being saved, but looks like I can't get those benefits without running the risk of saving passwords or being repeatedly asked, several times a day, whether I want to save the password (when the answer is always "No.").

I appreciate any further suggestions.

If you do not want to save passwords then disable the Password Manager.

• remove the checkmark:
  *Options/Preferences -> Privacy & Security: Forms & Passwords: "Ask to save logins and passwords for websites"

• https://support.mozilla.org/en-US/kb/password-manager-remember-delete-change-passwords