Doctor Who is a long-running British science fiction series which premiered in 1963. Matt Groening claims to be a fan of Doctor Who. Whenever the Doctor appears he is in his fourth incarnation as portrayed by Tom Baker from 1974 to 1981 (over its 50-year history, 13 actors have played the character on TV, but Baker is considered to be the most well known in the US). Thus far, the Doctor has had no speaking lines in any of his appearances.
References to Doctor Who in The Simpsons
In Treehouse of Horror X, Comic Book Guy, aka The Collector, had the Doctor concealed in plastic, along with many other geek-show characters. He introduces the Doctor as Doctor Who (a rarely used name of the Doctor) to Bart Simpson, aka Stretch Dude and Lisa Simpson, aka Clobber Girl.
Comic Book Guy is seen walking out of a taco shop with a hundred tacos, stating that they'll give him sufficient energy during the Doctor Who marathon.
Tom Baker appears in his Doctor costume in the episode "Mayored to the Mob".
In the season 24 episode "Love is a Many Splintered Thing", the Tardis shows up for just a moment in the British movie the kicked out men were watching.
The future Springfield depicted in Holidays of Future Passed featured Dalek policemen, complete with British constable hats and nightsticks.
In the episode Diggs, Diggs's cast with a list of people he wanted to visit included the Tardis and Dalek #7.
References to The Simpsons in Doctor Who
The Simpsons have also been referenced on the revived Doctor Who. In the episode Planet of the Ood, one of the Ood's programming functions is 'classic comedy': the Ood Operations worker says, "Ood, you've dropped something." The Ood replies with "D'oh!"
Also, in Tenth Doctor David Tennant's swansong episode The End of Time: Part 2, there is a possible in-joke: After being rescued, the Doctor is strapped to a wheelchair. As he's pleading with his rescuers to unstrap him, they wheel him down a flight of stairs. Halfway down, he shouts "Worst! Rescue! EVER!" very much in the manner of Comic Book Guy and his catchphrase.
In the novel, Vampire Science. Sam Jones' teacher, Mr Selby, once asked her who her role model was. She had answered 'Lisa Simpson'.