Our dog became quite attached to one of DS's rejected teddies when she was a pup and still takes it to her basket with her every night. It's one of those blanket/bear hybrids and she kneads it with her paws (like a cat "making the bread") and falls asleep with it in her mouth. I've never known a dog to do this before.
She also has a favourite stuffed Pug that is strictly for throttling. She likes to run around with it and do the "terrier shake". No other toy will do.
So much weirdness but so cute.