The doll from the Island of Misfit Toys. No one knows her deal, huh? Everyone else's misfithood is pretty much explained... jack in the box named Charlie, cowboy on an ostrich, bird who swims, train with square caboose wheels, etc. But we're left to wonder about the doll. There's nothing physically obvious to make her a misfit, so most folks assume the issue's mental. Maybe she's the doll that never stops crying, or maybe she wets constantly. We'll probably never know for certain.
But personally, I think she shivved a Mrs. Beasley doll and took refuge in the one place that wouldn't rat her out to the toy cops.