The End of the World: Although it might not be visible at first glance, it’s this story that it’s all coming from: human being who has, through attempting to combat the vicissitudes of age, been rendered into a grotesque quasi-human object on serious life support, who joins a group of people on a cruise over the Earth, starts picking them off one by one using killer robots, tries to aim the vessel at a heavenly body, and then, when caught, reveals it all to be a financial scam before being killed.
The Unquiet Dead: maid sacrificing herself for the hero.
World War III: Well-known television anchor makes guest appearance.
The Long Game: Hidden megalomaniac tycoon named Max; shielded layer of the ship/space station where nobody goes which hides a terrible secret.
Boom Town (and arguably Torchwood): Watch where the Tardis goes when it flies towards the Earth—it’s on a beeline for Cardiff.
The Parting of the Ways: person getting sucked out into space; character giving farewell message through blue-tinted projection.
The Christmas Invasion: Ambulatory seasonal ornaments which turn out to be killers; unseasonal snow caused by spaceship activities; a bit of gratuitous royal-family-baiting.
Tooth and Claw: More royal-baiting, plus a queen who knows who the Doctor is.
Rise of the Cybermen/The Age of Steel: Crippled megalomaniac businessman plotting takeover with evil army of robots; talking holographic advertising pictures with annoying catchphrase; Doctor gatecrashes posh party; companion in waitress uniform.
The Impossible Planet/The Satan Pit: Trapped people, trying to find their way out of a doomed edifice while being attacked by what used to be calm-voiced innocuous servant-beings and are now calm-voiced vicious killers; Tardis, which could provide a solution, is conveniently rendered hors-de-combat for the duration; somebody getting sucked into space; the commander is trapped in the control centre with no way of getting to the others. Unscientific adventures in magnetism.
Love and Monsters: The Doctor’s “Hold on! I can save her!” bit, with mixed results.
Fear Her: Yet more moonlighting news anchors.
The Runaway Bride: Santa’s a robot, yes, and so are the Christmas angels. More unseasonal snow. Gratuitous Gallifrey namecheck. One-off companion (though the chances of this one coming back in two seasons’ time are slim). Villain falling into bottomless pit at end. There's a review on Tachyon TV which draws pretty hilarious parallels between the two.
Smith and Jones: Another bloody companion who falls in love with the Doctor straight off, and manages to get a snog off of him.
The Shakespeare Code: More baiting of queens who know who the Doctor is.
42: More trapped people trying to find their way to the bridge; more people getting sucked into space, in this case grabbing the villain and taking them with them as they do so.
Human Nature: Yet another companion in Edwardian servant uniform.
Blink: Creepy unstoppable killer angels.
Catchphrasewatch: “I’m so sorry”; “Allons-y, Alonzo” (groan); “No no no no no no!” (ad nauseum).
Old Skool Who: The Robots of Death, a lot (beautiful art-deco robots who go on a strangling spree thanks to the intervention of an evil genius who’s smuggled himself on a long trip; practically every line the Host have which isn’t preceded by the word “information” is, or ought to be, copyright Chris Boucher, and by the time you get to a scene where one gets its hand first stuck, then cut off, in a door, you start to wonder if RTD isn’t just taking the St Michael); Enlightenment (human-seeming entities who have fun by flying Edwardian ships around the solar system and looking down on Earth humans); Delta and the Bannermen (alien tourists visiting Earth, incognito, having a fairly dubious grasp of the planet’s culture, and getting hit by a satellite; there’s even a tickling-stick visible on the Titanic as the Doctor leaves the Tardis); Revelation of the Daleks (disembodied-head bad guy who is secretly planning corporate machinations); while we’re at it, there are talking disembodied heads in Perspex tanks in the Peladon stories as well; The Claws of Axos (a horde of space-borne beautiful golden killers); The Web of Fear (unexpectedly deserted London); The Enemy of the World (it’s not the first time the Doctor’s teamed up with a blonde named Astrid); Earthshock (blobs representing people vanishing off the scanner screen as they get picked off one by one by robots; ship programmed to crash into the unsuspecting Earth). Silver Nemesis (Queen cameo). The Wheel in Space (controlled meteorites as weapons). Frontios (Human being incorporated into machinery that runs on wheels).
Everything Else: Real life (tycoon Robert Maxwell, who famously threw himself off his yacht when his company went under, or did he); Blake’s 7 (teleport bracelets, even down to the design; Mr Copper’s half-understood pastiche of Earth culture is like the President’s half-understood pastiche of Earth history in “Bounty”; “In-for-ma-tion”); The Poseidon Adventure (forget all other 70s disaster movies—this is the source, down to including a fat woman with a Shelley Winters hairdo); Star Wars: A New Hope (attempt to cross a chasm on a narrow beam, as army of killers tries to break through the door); Aliens (unexpected attack by woman wielding forklift); Alien 3 (same woman, hurling herself and the enemy into a fiery pit; Astrid even does a slow-motion look-up like Sigourney Weaver does); Seven Years in Tibet (the Doctor’s slow-motion walk through fire); any movie/TV show involving a talking disembodied head in a Perspex tank, from They Saved Hitler’s Brain through the future sequences of Blackadder’s Christmas Carol (where Nursey is now, well, you get the idea); Harry Potter (talking pictures); Ghost (touching sequence featuring kisses between phantom and corporeal people); Robert Silverberg’s novella “Elegy for Angels and Dogs,” which features a clique of superrich people who, at one point, sail through the Solar System on the Queen Mary liner, which has been converted for space flight); Goldfinger (gold people theme, plus compare the Angels’ halo-throwing to Oddjob’s hat trick). James Cameron’s Titanic (leaving aside the obvious, you’ve got an ending where the hero [Leo DiCaprio/Astrid] dies and the bad guy [Billy Zane/that rich fellow] lives; Douglas Adams’ Starship Titanic. There’s a film called “Passenger 57”.