When the Boys from the Dwarf lost four days of memories, they looked for the black box to determine what had happened. It was missing, but the boys followed it's signal to a moon, where they found the box buried in a shallow grave. Despite a warning recorded by Holly, Lister and Rimmer watched the recordings of their exploits from the missing days. They discovered that Lister had doctored Rimmer's memories to give him a past love affair, which Rimmer wanted removed when he discovered the deception. (RD: Thanks for the Memory)
Rimmer accessed the black box of the SSS Esperanto in order to determine why it had been abandoned. It listed the crew's work with genetic acceleration but cut off in the middle of their cataloguing mission. (RD: Back To Reality)
In order to discover what had befallen the ships in a spaceship graveyard, the Boys used their scouter to locate the black boxes. They showed harrowing images of viscious GELFs called Psirens tricking and devouring the crews. (RD: Psirens)
Red Dwarf's black box was ejected by Holly shortly after the radiation leak had killed the crew and eventually splashed down in the Pacific Ocean. Through this, Michael McGruder knew that his father had been revived as a hologram. (Last Human) This same premise is used for the Space Corps Database on the official Red Dwarf website, except laid out more from the perspective of the crew in Series VIII, and being somehow sent back through time and space.