I've always paid to have my pets cremated, not crazy about the idea of burying them in the yard. When we bought our first home, I was puttering around in the back yard with my dog, planting some flowers around the little 'doll house' storage shed. While squatting on the ground, I turned around to check on my pup and I saw part of the head of a Doberman sticking out of the ground. An old woman owned the house before us, and she probably didn't have the strength to dig a deep enough hole.
Anyhoo, I freaked out and grabbed my dog by the collar and took him into the house asap. My husband was out of town on business, so I ended up calling Animal Control and asking them to come and take the body. They were great, came very quickly and took the dead dog away.
I don't save the ashes from cremation, but I have saved a couple of paw prints in clay from two of my dogs who were euthanized.