Why do some people like to intimidate others?

What is a person trying to do, when they intimidate others. I have encountered people like this. Usually it’s someone in the work place. I used to let them intimidate me, because of a job, etc. but I soon learned that no one had the right to do this to me. When I spoke up to them it stopped. I since have felt intimidated among friends or family at times. I have also used the same approach, telling them that I do not appreciate their harshness. It doesn’t seem to work very well, I’m afraid. I’ve tried ignoring them as well. What else can I do, to get them to stop intimidating me?