When we bought our house about 5 years ago the previous owners warned us about Cookie, a neighborhood squirrel. She was easily recognizable because she had a stumpy tail and was almost tame. (They had been feeding her for a couple of years and she had clearly become accustomed to it.) She'd be waiting by the back door when we went outside, keep me company while gardening and would follow us around the yard with an expectant look in her eye. She even knew the sound of Mike's car and would meet him in the driveway after he came home from work.
Mike, of course, bought her bags of unsalted peanuts and quickly earned himself the nickname of "The Squirrel Whisperer." Cookie quickly learned to come when we called her name, to take a peanut from our hand and, in exchange, let us watch her closely as she ate - our clever little outside pet.
The last time we saw Cookie two years ago, it was winter and she was heavily pregnant. She sat on our back steps, ate a few nuts and then was gone. We never saw her again but we suspect at least one of her litter survived...