Is it common for animals to stand perfectly still?

I glanced out of a window and saw what appeared to be a squirrel, but it was perfectly still. I walked over to the window to take a closer look, and it was indeed a squirrel. It must have stayed in that position for two or three minutes, not twitching a muscle, staring straight ahead. I am used to seeing squirrels in constant motion, so it struck me as a bit odd.

I have previously seen other animals do this for a long stretch of time, a rabbit one time and a Canada goose in a wooded area near a stream. Is this a way for an animal to rest while remaining alert to predators?