The Doctor

The Doctor is the protagonist of the British TV series Doctor Who. A Time Lord from the planet Gallifrey, the Doctor is a time-traveller who travels around the universe in the TARDIS, a time machine, and saves lives.

So far, the Tenth and Eleventh Doctors have appeared in HISHE.

Doctor Who: How Doomsday Should Have Ended
The Tenth Doctor is seen inside the TARDIS bidding farewell to Rose Tyler at Bad Wolf Bay. He begins to say his parting words, but his connection to her fades, so he tries to reestablish the connection, promising to talk to Donna Noble next. He tries to say goodbye to Rose one last time, only to be interrupted due to the stars he is using burning up quickly. After foiling an attempt at his life from Daleks, the Doctor finally says that he loves Rose, but realizes that he's a Time Lord and she's in another dimension, so it will never work, and muses that he might clone himself. River Song then walks by, saying, "Spoilers!"

Super Café: Who's a Hero
After the events of "The Name of the Doctor," the Eleventh Doctor visits the Super Café to discuss the events with Superman and Batman. He clarifies that as a superhero for the universe, he decided to visit the café to say, "You're welcome." Superman is skeptical, but the Doctor explains that Krypton's fate was not to be tampered with. Batman notes that this is just as convenient as the Doctor's sonic screwdriver, and complains that the Doctor could have saved Rory and Amy. The Doctor then notes that he might do what he's always been doing and probably get a new body. Superman decides to help the Doctor in case a Dalek arrives, but the Doctor notes that it's impossible to snap a Dalek's neck since they don't have one anyway. As Batman laughs with the Doctor, Batman says, "No, seriously, go back and save Amy."

In the end credits, the Doctor finds Batman somehow inside the TARDIS and flirting with Clara Oswald and shoos him away.

Trivia

 * Due to the concept of Time Lords being able to regenerate their bodies upon near death, the Doctor has been played by a variety of actors. William Hartnell, Patrick Troughton, Jon Pertwee, Tom Baker, Peter Davison, Colin Baker, Sylvester McCoy, Paul McGann, Christopher Eccleston, David Tennant, Matt Smith, Peter Capaldi, and Jodie Whittaker have played the Doctor as series leads, while Michael Jayston, John Hurt, and Jo Martin have played other versions as supporting roles.
 * Although the Eleventh Doctor says that he could get a new body soon, The Time of the Doctor reveals that at this point in the Doctor's life they have already run out of regenerations (the Eleventh Doctor is technically their thirteenth incarnation, with the War Doctor and the Tenth Doctor's regeneration into himself counting as full regenerations).