Cultural references to the Doctor Who universe

Just as characters from other fictional universes have appeared in the Doctor Who Universe, elements of the Doctor Who Universe, have (for the most part, unofficially), appeared in other continuities.

Partial list

Television

Get Off My Cloud, the final episode of the third season of the BBC's anthology series Out of the Unknown was partly set in the subconscious mind of a science-fiction writer and featured in-character appearances by the Daleks as fictional creations inside the mind of the writer. (The episode's designer was Raymond Cusick, who was earlier responsible for the original Dalek design.)

Arrivederci Roma, the first episode of the first season of Channel 4's comedy series Chelmsford 123, showed the TARDIS materializing in the background of one scene, the Doctor briefly stepping outside before going back in and dematerializing.

The Fourth Doctor has appeared several times in The Simpsons.

Green Courage, an episode of Fox Kids' children action series Power Rangers Lost Galaxy, featured an on-screen note claiming that a meteoroid field that had just collided with a planet was located at "ten zero eleven zero zero by zero two from galactic zero," in the constellation of Kasterborous. These are the same coordinates as stated in Pyramids of Mars as the location of Gallifrey.
In 420, an episode of Family Guy, Brian says that ever since weed was legalized "crime is down, productivity is up, and the ratings for Doctor Who is through the roof". Another Family Guy episode, the Star Wars Episode IV spoof "Blue Harvest", incorporated footage from the Tom Baker-era opening credits during the scene in which the Millennium Falcon enters hyperspace.
Several episodes of the 2008 series The Middleman include references to Doctor Who. For example, in one episode a character is identified as "Lethbridge-Stewart". Only 12 episodes were produced, with the decision made not to produce a 13th episode. That episode, The Doomsday Armageddon Apocalpyse, also contained several references to Doctor Who, most notably having the Middleman recite the First Doctor's farewell speech to Susan Foreman in The Dalek Invasion of Earth ("There must be no regrets, no tears, no anxieties..."). The script for this unmade episode was performed by the cast in a "read through" at the 2009 San Diego ComicCon and also adapted into a graphic novel by Viper Comics, both with the Doctor's speech intact. Given the series' acknowledged debt to Doctor Who, the fact the lead character is never referred to by name, only as "The Middleman", is a probably reference to the fact The Doctor's real name is never revealed. (The aforementioned finale episode, however, does reveals the Middleman's real name.)
In the fifth episode of the second season of the ABC television series Better Off Ted, the scientists Phil and Lem name the small robot designed to clean up spills in their laboratory Chumbley, the same name that Vicki gives the robots that she, Steven, and the First Doctor encounter in the story Galaxy 4. Later on in that same episode, Phil and Lem enter a room full of used robot parts where a Dalek can clearly be seen in the corner nearest the door.
Several episodes of Leverage reference Doctor Who, including one in which Nathan Ford is asked what ID's he has on him so that he can board an airplane. He replies, "I've got a Peter Davidson, Sylvester McCoy, and a Tom Baker." Sophie adds, "I've got a Sarah Jane Baker." Hardison pronounces them man and wife. Another episode had Hardison mentioning that he had been torrenting the latest episode of Doctor Who.

Comics

Marvel UK

Marvel UK created a number of characters who appeared in various titles owned by the company, including Doctor Who Magazine (which was later re-named Doctor Who Monthly). The characters of the Special Executive (troubleshooters employed by the Time Lords, who had appeared in 4-D War and Black Sun Rising) appeared with Captain Britain in the "Jaspers' Warp" storyline written by the Special Executive's creator, Alan Moore.
The Doctor Who comics version of Merlin also appeared briefly in Captain Britain in a sequence demonstrating that Merlin had several alternate appearances and personalities that he could adopt as he saw fit. The Doctor has also appeared in cameos in several prose novels based in the Marvel Universe.
In The Crossroads of Time, published in Doctor Who Magazine, the Seventh Doctor ran into (literally) Death's Head, who was departing the Transformers universe; he sent Death's Head on to the future Earth of Dragon's Claws (a Marvel UK title that may be set in the Doctor Who Universe, since Dogbolter and Keepsake are both residents of this Earth). Later, the Doctor guest-starred in Death's Head's comic book from Marvel UK, a crossover that ended with the Doctor depositing Death's Head in the main Marvel universe (Earth-616) atop the Fantastic Four's headquarters, Fours Freedom Plaza - providing a direct link between the Doctor Who Universe and Marvel's Universe. Death's Head himself interacted with mainstream superheroes from the Marvel Universe, which provides another, indirect, link between the mainstream Marvel Universe and the Doctor Who Universe.
Both Reed Richards of the Fantastic Four and Alistaire Stuart of Britain's Weird Happenings Organization (WHO, a nod to Doctor Who) have obliquely mentioned being friends of the Doctor.
JLA Classified #1 reveals that Batman keeps a Dalek in his "Sci-Fi" closet.

DC/Wildstorm

The Wildstorm title Albion, scripted by Leah Moore and plotted by her father, Alan Moore, featured a Cyberman and also an Ice Warrior. It is unclear whether the Cyberman was meant to be 'real' or a costume. (The scene was set in an SF-themed bar, but the 'real' Robot Archie is also on display.) Like The Establishment, which featured a Doctor Who pastiche characer, Albion was deeply rooted in English popular culture.

2000 AD

The 2000AD strip Caballistics, Inc. features Doctor Who references so often that they are practically part of the series' format. However, it also depicted a character clearly intended to be the actor Tom Baker being murdered by Scottish nationalist demons. This would appear to undermine the frequent suggestion by Caballistics, Inc fans that the series is unofficially set in the Doctor Who universe.

The League of Extraordinary Gentlemen

Alan Moore's crossover series The League of Extraordinary Gentlemen links the Silurians to the Creature from the Black Lagoon. Additionally, the TARDIS appears in the background of The Black Dossier.

Buffy the Vampire Slayer

The Doctor and Rose Tyler can be seen in Part 1 of the season 8 comic No Future For You.

Prose

Barbara Hambly's Star Trek novel Ishmael contains a number of references to Doctor Who and a cameo appearance of the Fourth Doctor and Leela.

Lady Jennifer Buckingham from The War Games appears in the second volume of Kim Newman's crossover-intensive Anno Dracula universe. Charles Beauregard, the hero of several Anno Dracula stories, is referred to in All-Consuming Fire. One of Newman's books in the Dark Future series makes references to an alternative timeline, ultra-nationalist pro-English version of the Doctor Who television series in which the Doctor makes visits to famous events in English history while fighting off extraterrestrial threats to the Crown. Newman's Life's Lottery, a playful exploration of the concept of alternate universes, references Inferno in some detail (and a character fantasises somewhat colourfully about Jo Grant).

Michael Moorcock, an admirer of Doctor Who, had "Doctor Who" and a Dalek appear, amongst many other fictional characters, in his The Condition of Muzak.

Richard Calder's Dead trilogy features numerous dark alternative time lines involved in a sex war between men and woman, at least one featuring a version of Doctor Who. The last scene of the final volume, Dead Things, shows the young protagonist watching a scene of the "Daleks exterminating the slave girls of Skaro" on television.

The Red Dwarf novels have a number of references. Kryten, for example, owns a sonic screwdriver.

Video games

Lemmings 2: The Tribes

The exit for the "Shadow tribe" level is clearly the Doctor's TARDIS.

Out-of-universe references

A number of TV series have made reference to the Doctor Who franchise itself:

Sheldon from The Big Bang Theory has said that he wakes up and watches Doctor Who every Saturday morning.
A 2009 episode NCIS, "Power Down", includes the character of McGee comparing the unexpectedly spacious interior of a cargo container to the TARDIS, and briefly explains the meaning to another character, who replies, "Doctor Who - who watches that?"
A reference to Doctor Who also occurs in the CSI: New York episode "Time's Up."
In the Christmas special in which the title character of The Vicar of Dibley got married, her bridesmaids were dressed as the Tenth Doctor and two Daleks.
In an obvious reference, the 13 May 2010 Episode of CSI: Crime Scene Investigation is titled "Doctor Who."