The Hitchhiker's Guide to the Galaxy (in-universe)

The Hitchhiker's Guide to the Galaxy was a series of books, as well as a radio series, television series and a film from the late 20th and early 21st century that was referred to by the Doctor and others on a few occasions.

The Seventh Doctor once asked, rhetorically, who had said that "Earthmen rarely invite their ancestors to dinner", which comes from the series. (DW: Ghost Light) The Tenth Doctor once compared himself to Arthur Dent after saving the Earth from invasion in a dressing gown (Dent's trademark dress), and after being awoken from his post-regenerative coma by tea, the character's favourite drink. (DW: The Christmas Invasion) The number 42, which in the Hitchhiker's books was the answer to the question of life, the universe, and everything, was one of the numbers the Tenth Doctor guessed when trying to find out the security protocol for the the Host. (DW: Voyage of the Damned)

When Professor Chronotis stole The Worshipful and Ancient Law of Gallifrey from the Panopticon Archive, he replaced it with another book, which he described as "an Earth classic by one of the greatest writers in that planet's history. ... Terribly funny, terribly thoughtful, wish I could remember the name of it, something about thumbing a lift, and there were towels in it ... oh yes, of course, it's called The Hitch—" before being interrupted. (DWN: Shada)

Rory Williams referred to the asteroid he travelled to as "the junkyard at the end of the Universe", a reference to the setting and title of, the second book in the Hitchhiker's series. (DW: The Doctor's Wife)

Real world connections
Hitchhiker's creator Douglas Adams wrote a number of Doctor Who serials and served as its script editor for Season 17. Consequently, lines from Hitchhiker's Guide (including the famous instruction "DON'T PANIC") found their way into DW: The Pirate Planet, while Hitchhiker's character Oolon Coluphid and Betelgeuse gets a mention in DW: Destiny of the Daleks, which Adams script-edited (the Doctor is seen reading one of Caluphid's books, Origins of the Universe). Another possible reference is the name of the planet Bandraginus V whose name closely resembles Santraginus V, a planet from Hitchhiker's. (DW:The Pirate Planet) The storyline of Adams' Life, the Universe and Everything was based on a rejected Doctor Who script called Doctor Who and the Krikkitmen. Adams later reused the character of Professor Chronotis in his novel.

Because Paddy Kingsland did special sounds for both the Hitchhiker's Guide radio programme, and for The Sun Makers, there are sounds which are common to both productions. Notably, the sound of the Fourth Doctor fiddling with a combination lock in part 4 is the same as the sound heard in Hitchhiker's whenever the Guide itself was being consulted. (DCOM: The Sun Makers)

Just prior to becoming the Fifth Doctor, Peter Davison made a cameo appearance in the BBC's 1981 adaptation of the first book as the "Dish of the Day". His wife, Sandra Dickinson, played Trillian in the miniseries.

Actors shared by the Doctor Who and Hitchhiker's Guide franchises
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Crew shared by the Doctor Who and Hitchhiker's Guide franchises
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Metafictional parallels and references

 * The plot of DW: Voyage of the Damned is similar (but not identical) to that of "Starship Titanic", a video game authored by Adams which was published in 1998. Both feature a large luxury spaceship/cruiseliner named "Titanic" which goes out of control and whose computers must be manipulated to fix the ship. The video game was based on a brief mention of the ship in the first Guide book, which was unable to send out its first and only message - an S.O.S. - during its launch before suffering a "total existence failure".
 * DW: 42 shares its title with the Answer to Life, the Universe, and Everything, as revealed in Adams' Hitchhiker's series. As with the spaceship stolen by Arthur Dent and friends in The Restaurant at the End of the Universe, the ship in 42 is on its way to crashing into a star, leaving its passengers with no escape.
 * The reference to Oolon Coluphid has raised speculation as to whether the Doctor Who universe and that of the Hitchhiker's Guide are one and the same. Another matter blurring the lines between the Hitchhiker's universe and the Whoniverse is the Tenth Doctor's early reference to Arthur Dent being a "nice man" who saved the universe in "his jim-jams"; it's left ambiguous as to whether he's referring to a fictional character or a real person. (DW: The Christmas Invasion) Also, it is mentioned in Doctor Who (though not proven or brought up further in any later episode) that humans may have evolved from an extraterrestrial species. (DW: Image of the Fendahl) This might have some relation to the idea of humans being descended from Golgafrinchans in Hitchhiker's Guide.
 * Perhaps by a coincidence, the scene in the third book of the quintilogy (later adapted into a radio script of the same name) Life, the Universe, and Everything, in which Arthur Dent and Ford Prefect, materialise in Lord's Cricket Ground, is similar to a similar scene in The Daleks' Master Plan in which the First Doctor materialised his TARDIS at The Oval.
 * On the second DVD disk of The Hitchhiker's Guide to the Galaxy TV series, a TARDIS in policebox form can be seen tracking the ship upon which Arthur is getting a lift, during the opening credits of the 'The Making of...' documentary.
 * One of the spaceships in BFA: Max Warp is described as a "Lazlar Lyricon custom job". This is how one of the spaceships in the Milliways car park in episode 5 of HHGG was described.
 * As highlighted by the BBC official Doctor Who website, there is a copy of The Hitchhiker's Guide to the Galaxy in the Library as seen in Silence in the Library.
 * When Adams' unfinished television story Shada was remade by Big Finish Productions, writer/producer Gary Russell introduced a few references to the Hitchhiker's series as a tribute. These included making the car which Skagra steals into a Ford Prefect (and its owner the treasurer of the Ford Prefect Appreciation Society), and, in the webcast version, showing a Nutrimat machine in the background of the lab and silhouettes of Zaphod Beeblebrox and Arthur Dent as two of the prisoners in Shada. (WC: Shada, BFA: ''Shada)
 * Similarly, when author Gareth Roberts novelised Shada in 2012, he added a reference to Professor Chronotis having replaced The Worshipful and Ancient Law of Gallifrey with a copy of The Hitchhiker's Guide to the Galaxy (see above). (DWN: Shada)