This poor bunny has head tilt/torticolis. This can be cause by ear infections, even the horrible EC parasite. If you see a bunny looking like this, DON'T think its cute, get it vet treatment! Head tilt can be permanent, and very miserable!
For most of the animals on this list, their long hair or fur evolved as a way to cope with the cold. Others were bred to have long hair, and some of these are not even capable of surviving on their own in the wild because of it like the Angora rabbit.