We weren't allowed to have stuffed animals when we were very young, because my mother felt they were un-hygienic, and would cause health problems. (Yes, mom was a bit of a clean freak, and also pretty controlling.)
But I did get my own stuffed animals later when I had my own babysitting money. And it seemed boyfriends always gave me stuffed animals, as gifts.
I have a large-ish polar bear that I named Eric, three bunnies, a koala named Mike, and an Opus, the penguin from Bloom County (a comic strip from the 80's). All my cuddlies make me happy to see them. They hold happy memories.