Douglas Adams first mentioned the Starship Titanic in the third Hitch-Hiker novel Life, The Universe and Everything - a prototype Improbability Drive ship that unfortunately suffered a gratuitous Total Existence Failure during its maiden voyage. Terry Jones' novel "Douglas Adams' Starship Titanic" develops this story arc further in parallel with the computer game.
Doctor Who is indebted to Douglas Adams in many ways and the Russell T. Davies and Steven Moffat series are laced with references to Adams' books. The 2007 extended episode Voyage Of The Damned, starring David Tennant and Kylie Minogue, was also set on a Starship Titanic, although arguably the plot itself had more in common with The Poseidon Adventure. This Titanic was once again staffed by mad robots - robotic angels with deadly, detachable halos.
Douglas Adams has a history of developing brilliant but tricky computer games - his two Interactive Fiction games, Bureaucracy and the official Hitch Hiker game, are both masterpieces of fiendish multi-layered puzzles. Success is virtually impossible but failure is fun. I don't know what happens if you complete either one of them - possibly the entire Universe is destroyed and replaced by something even more fiendish (there are of course those who claim this has already happened.) You can play a version of the Hitch Hiker game here on the BBC Radio 4 website, updated with some fantastic new artwork. The original text-only game is hosted here.