An alien behemoth known as Doomsday killed Superman. After a three-month hiatus on all Superman titles, all of them were relaunched with four new heroes, each claiming to be Superman reborn in some way. Eventually, of course, the real Superman returned after being regenerated in the Fortress of Solitude.
In Superboy #124, Lana Lang rescues an alien visitor who has gotten himself trapped under a fallen tree. As her reward, Lana is given a ring which endows her with insect-like abilities. She quickly decides to use her new powers to begin a career as a super-hero and settles on the name "Insect Queen".
While other members of the Superman family simply ceased to exist, Supergirl actually dies in Crisis on Infinite Earths #7. According to Marv Wolfman, "Before Crisis it seemed that half of Krypton had survived the explosion. We had Superman, Supergirl, Krypto, the Phantom Zone criminals, the bottle city of Kandor, and many others. Our goal was to make Superman unique. We went back to his origin and made Kal-El the only survivor of Krypton. That, sadly, was why Supergirl had to die."