When I still lived with my parents, the garage door accidentally got left open one night, and a possum got in. It jumped out at my dad when he went out to feed the cats in the morning; it was inside the big bag of cat food. Scared him half to death! We borrowed a no-kill trap from my sister's boyfriend to catch it, and then she and I drove it out to a rural area and let it go, but it kept trying to bite us as we were trying to open the cage. It was really creepy.
I'm sure some people do have squirrels as pets, probably wild ones that they rescued as babies and kept. You can't buy them in pet stores or anything, as far as I know.