8. Punky Brewster
As a child of the eighties, this is my first memory of the baby born in the elevator trope, even though it wasn't the actual first sitcom to do so. Punky and her friend Cherie are trapped in a hospital elevator, and the baby magically pops out seconds before the power to the elevator is restored and doctor arrives. Of course the real good deed here was that Punky and Cherie kept the baby from being named Herman.