The final disposal of the body of a pet dog is a delicate and often painful subject that you should discuss prior to euthanasia to ensure that your wishes are carried out appropriately. The remains of dogs without owners, such as shelter animals, are treated more practically and with less sentiment, but hopefully with no less respect.
Cremation -- burning to reduce the body to ashes -- is the most common way of handling the bodies of small animals after they are euthanized. This is done in a special incinerator that renders the ashes sterile if the dog had a contagious disease. It can be done en masse at a shelter, hospital or community facility if there are multiple bodies, or on an individual basis at a private facility by a pet owner who wants the cremains returned. There is usually a fee for private cremations, based on the weight of the dog, and a selection of urns to hold the cremains may be offered for sale. Ashes may be scattered at home, in a park, at sea or anywhere else the pet owner wishes.
Burial in a pet cemetery or on private property is another option. Pet coffins, from simple to elaborate, are available online and through pet stores, but "green" or natural burial -- without embalming, casket or crypt -- is available at some special park-like pet cemeteries. Home burial is possible for a dog who had no communicable disease, depending on local ordinances, as long as it is on privately-owned land and is carried out appropriately to avoid contamination of the environment.
Some veterinary schools accept the bodies of euthanized dogs to be used as anatomy cadavers for students to learn from, but this is according to the individual school's needs, which may be limited and quickly filled. The bodies of pet dogs euthanized for medical conditions of special interest are usually accepted readily because the dog's medical history is known, enabling students to learn in greater depth from the original diagnosis and previous care.
Beyond traditional taxidermy, which does not always have optimum results, some dog owners choose to have their pet's body preserved as a memorial. The freeze-drying techniques used in this method are improving with increased demand as this developing option gains popularity.