What is the button called on phones that the handset rests on?

Question

The one that hangs up the phone when it's down... that you'd press if you needed to get the line to make a new call....

Answer 1

Most people call it the hook.  You've heard the phrase, is the phone off the hook?  On the older older phones the handset actually sit on a metal arm shaped similar to a hook.

The term just never lost popularity.

On hook = hung up

Off hook = not hung up