Mange is the name for an infestation of parasitic mites and characterized by skin lesions, itching, and loss of hair. There are many different types of mites that cause mange; as far as I am aware they all belong to the Suborders Astigmata and Prostigmata of the order Parasitiformes.
The two most well known types of mange are Sarcoptic Mange and Demodectic Mange. There are others, including Notoedric Mange, Psoroptic mange, Cheyletiella Mange, and Chorioptic Mange. There are forms of sarcoptic mange that can infest humans, and it also appears in dogs; hence its fame. Demodectic mange also appears in both dogs and humans, among other animals, but is not contagious and so is less common.
Due to the complexity of all these manges, you should probably go to the specific nodes in order to learn about specific types; here I will include a list of synonyms to aid you in finding your way around.
Sarcoptic Mange
Scabies, Seven Year Itch (Humans)
Canine scabies (Dogs, foxes)
Hog mange (Pigs)
Barn itch (A number of large barnyard animals)
Demodectic Mange
Demodecosis, Demodex, demodectic acariasis, follicular mange, and red mange.
Notoedric Mange
(Primarily in cats) Feline scabies and face mange.
Psoroptic mange
Sheep scab (Sheep, cattle, horses)
Rabbit ear mite (Rabbits)
Cattle scabies (Cattle)
Also, body mange, ear mange
Chorioptic mange
Foot scab, heel mites tail mange, leg mange, itchy
leg, and scrotal mange.
This is a work in progress, as I try to node as many types of mange as I can. This node should have waited until I had noded a few more, but Hippie's WU, claiming that 'Mange = Demodectic Mange' provoked my into early posting.