Apparently some veterinarians used to keep a few dogs and cats in their facilities for the express purpose of blood donation in emergency situations. There are now national, regional and local veterinary blood banks. And some people make their pets available as local donors. Dogs have about a dozen blood type groups and cats have three groups with some variation within each group. Generally the donor and recipient animals must be matched, though dogs with A negative blood are universal donors.
Cats have no universal donors, but almost all domestic shorthair cats have type A blood.
Horses have more than 15 different blood types, way more than humans. When needed for medical emergencies and other equine surgical procedures requiring blood replacement, veterinary assistants load Beevo up and transport the horse a few miles south to the OSU Veterinary Hospital on campus. The horse has donated blood up to nearly three quarts a pop when necessary for a single complicated surgery scores of times during the past several years. Apparently he doesn't balk too much at the procedure. They do sedate him a bit while they draw blood from his jugular vein.