In the past, the hospital test for pregnancy was to inject a rabbit with the woman's urine. During pregnancy, and ONLY during pregnancy, a woman secretes a hormone called hCG. This indicates that an egg has been fertilized.
hCG is released into the urine. When the urine is injected into immature female rabbits, the rabbit's ovaries show signs of being sexually mature, thus indicating the woman is pregnant.
Unfortunately, in order to examine the ovaries, they must be surgically removed to be examined. Now, the rabbits could be sewn up and left to heal, but then someone has to pay for the surgical recovery of the injured rabbit until it can be used again. This was considered too expensive, so the rabbit was killed or allowed to die after the pregnancy test was completed. But the general public was told that the urine killed the rabbit, when in actual fact it was euthanized.
In the real world, when a woman's friend new she was being tested, they would often ask, "How's the rabbit?". and she would tell them, "The rabbit died."
With new chemicals tests, using a rabbit is no longer necessary. At home, you can buy a test at the drugstore, and just pee on the stick. Of course, in the hospital, they use a much more sensitive test.
[I've also heard jokes about women peeing on rabbits.]