The most common is the pet with an incurable, terminal illness such as kidney failure or certain types of cancer. These pets are usually older animals, and have been a part of the client's life for many years. The human-animal bond in these cases is incredibly powerful, and the emotional attachment to the pet can be overwhelming for the owner. In these situations, euthanasia is a quality of life issue. If the answer to both of these questions is no, then euthanasia should be considered.
Problems arise in defining quality of life.
This is a determination that must be made on an individual basis, and every pet owner's definition is different. I think two important criteria to evaluate are the pet's appetite and mobility. If an animal is not eating, and not able or willing to move about, then quality of life is likely poor. An owner must draw upon the years of interaction with the pet in order to form a reasonable evaluation of its quality of life. I also know that attempts at treating some conditions will be fruitless, and simply serve to prolong an animal's life, without regard to the quality of that life.