If you ask a child, stuffed animals are more than cuddly little pillows with arms and legs. If you ask a child, that's not a stuffed animal, that's Kimbo the lion, and he's allergic to milk, even though he loves ice cream. To an imaginative child, a stuffed animal is more than something to cuddle, it's something to love and endear with a unique personality and create a whole history for, something to go on adventures with.
As we've seen, this is a popular theme for stories about children. Of course, there's Calvin and Hobbes, about the rambunctious six year old with a pet tiger. On first reading, the premise seems to be that Hobbes is a stuffed tiger, but a real tiger in Calvin's imagination. To any long time reader, it becomes apparent that this is not the case. Hobbes is a real tiger, except for when grownups are seeing him. This is a pretty accurate representation. It's not that stuffed animals are not real, it's that nobody but their owners can see how real they are.
An earlier example is, of course, Winnie the Pooh. Christopher Robin, the only human character we see in AA Milne's original Winnie the Pooh books, has created not only a personality for each of his treasured stuffed friends, but an entire world for them to inhabit, showing how rich a child's imagination can be when creating a dramatis personae and a story for their stuffed animals.
It may not have been the original stuffed animal, but the Teddy Bear is probably the one seen as the most iconic (as well as being Winnie the Pooh's particular breed). As most of us know, the Teddy Bear was named for Theodore Roosevelt, inspired by an incident wherein Roosevelt had refused to kill a black bear which his hunting party had tied to a tree, on grounds that slaying a bound quarry would be unsportsmanlike. Originally named "Teddy's Bear", the animal has been immortalized as a stuffed animal and attributed with a variety of personalities and histories by just as many children (and even several grown up bear collectors).
After a certain age, most children seem to lose interest in their stuffed animals. The secret we all keep is that these creatures are immensely important to us, and even when your kids become too old to receive stuffed animals as gifts, very few young teenagers would be willing to part with the treasured friends they kept as small children. Even into adulthood, few people are willing to completely part with treasured stuffed animals.
Perhaps one thing that makes stuffed animals so special is that, unlike action figures and such, which come pre-packaged with their own character and stories, a new stuffed animal is usually anonymous and without a story upon arrival. It becomes almost an imperative responsibility for a child to give their new friend an identity.
At the right age, a child will develop a real, honest bond with a stuffed animal. When we're grown up, people see this kind of thing as eccentric or crazy, but for children, it's a completely healthy way to empower one's imagination, to learn about human interaction, and to find comfort and friendship where most people see buttons and stuffing.