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 took a space walk and found the box buried in a shallow grave with a gravestone dedicated to Lise Yates. 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. (Thanks for the Memory, Series II)
When Red Dwarf picked up an adrift cryogenic escape pod, the Black Box of the pod revealed its history. Inside was the lone survivor of a riot aboard a prisoner transport vessel containing murderous Simulants, that had originally been destined for the space prison Justice World. However, the Dwarfers could not ascertain from the Black Box exactly who was in the pod - a Simulant Convict, or a female human guard named Barbara Bellini. The Dwarfers decided it would be safer to go onto Justice World and open the pod there, although this course of action led to its own problems. (Justice, Series IV)
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. (Back to Reality, Series V)
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 vicious GELFs called Psirens tricking and devouring the crews. (Psirens, Series VI)
Whilst cruising in Starbug 19, the Dwarfers came across a Mercenoid transport ship which was locked into a death dive, kamikaze-style, into the heart of a super-massive Black Hole. Although Rimmer was scared and suggested that they leave the transport to its fate, a prisoner had also been detected aboard the transport, which Lister wanted to rescue since it could have been a human. They docked with the transport, disabled the Mercenoid, took it's Black Box, and rescued the prisoner before leaving the transport to fall into the Black Hole. Unfortunately, after returning to Red Dwarf, Kryten studied the Black Box in the Science Room and realised that the prisoner was actually a polymorph, and that the Mercenoid had actually been deliberately piloting the transport into the Black Hole to kill the polymorph. (Can of Worms, Series XI)
In the different continuity of the novels, the Black Box of Red Dwarf was ejected by Holly shortly after the radiation leak had killed the crew and eventually splashed down in the Pacific Ocean on Earth. 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.