Good question! Yes, there will be times when Facebook will ask for our password, however as Emil Protalinski from the article “Facebook will never request your password over email” mentions, they have changed their terms to read:
I got an email asking for my Facebook password.
Do not respond to this email. Facebook will never request your password over email, and we advise against providing your login information to anyone under any circumstances.
Before their terms did not include the “over email” part because they actually do ask for your password when users navigate to Facebook’s Update Your Security Information webpage. This was also explained in his handy article since it confused users. Here’s his original Facebook Password article. Basically he says it appears that it’s a major bug or flaw since it’s scaring people into thinking it could be some kind of a phishing scheme. Anyway, now you can be safe and know that Facebook does in fact ask for your password on their website. Just be sure the URL is definitely from Facebook!