What is an example of an appeal to fear?

An appeal to fear can be any form of speech or writing intended to sway people to a particular belief, action, etc. by making them afraid, especially if there is little or no justification for the fear.

A classic example of appeals to fear would be Nazi Propaganda that claimed the German way of life was under attack from various political and ethnic groups. Many people became willing to accept Dictatorship as a way to supposedly keep them "safe".