What's the simplest free (or cheap) software to remove unwanted motion in video footage?

Problem

I used a program 7 or 8 years ago, that stabilized a video by letting you select a part of the footage that was not supposed to move (like, a sign on a building, or a picture frame on the wall, etc). I remember that the cost was $100, I didn't buy it because my need at that time was very simple and…