This one's kind of work-in-progressy, so check back over the next few days as I'll be putting things in as they occur to me.
Rose: Another zoom-in on Earth/UK/London (see also Smith and Jones, etc. etc. etc.). Dropping a phial of Essence of Whatsit into the menace destroys or disrupts it.
Aliens of London/WW3: A pair of normal human beings are in fact green aliens with a secret agenda, and finding their human disguise uncomfortable.
Dalek: The Dalek is healed by a brief contact with Rose's DNA, just as the Master is brought to life through a brief contact with his wife's.
The Empty Child/The Doctor Dances: Alien medical device fetches up on Earth, which uses whatever's in it as a template to "repair" the rest of the human race, and so winds up turning everyone around it into a copy of one particular individual.
Bad Wolf (and later "The Stolen Earth"): Army of chanting Daleks rising on hover platforms = army of chanting Time Lords rising on hover platforms.
The Christmas Invasion: Mind-controlling a certain percentage of humans on Christmas Day.
Rise of the Cybermen/The Age of Steel: A menace which preys upon the homeless.
School Reunion, also Doomsday, Journey's End, The Sarah Jane Adventures etc.: Apparently once you've had Gallifreyan, you never go back, as Donna's perfectly functional relationship with an evidently sweet guy is described as "settling," just because he's not the Doctor.
The Impossible Planet/The Satan Pit: Ood whose eyes glow red in the presence of evil.
The Idiot's Lantern: Woman who talks to certain people through the television. Oh, and "Hungry!"
Love and Monsters: The Silver Cloak are basically a pensioner version of the find-the-Doctor club in this story, plus the whole "I'm not a Slitheen, I'm a related species" bit is echoed by the two cactus-heads to explain why they're nothing like Bannakaffalata.
Army of Ghosts/Doomsday: the whole setup with the Eternity Gate, down to two technicians who keep finding contrived excuses to run off with each other. Plus figures from the series' past, believed dead, but actually about to burst out of some secret hiding-place and take over again.
The Shakespeare Code: The Doctor and Queen Elizabeth I have a, shall we say, history together.
Last of the Time Lords (if only): Time Lord restoring self to normal through the concentrated belief of people.
Voyage of the Damned: Gratuitous cameo from a Queen Elizabeth II impersonator = Gratuitous cameo from a President Obama impersonator.
Planet of the Ood: They've got a functioning civilization now, apparently, although they're still carrying their brains around in their hands.
The Sontaran Stratagem: A deleted scene has the Master complaining pedantically about the phrase "merry Christmas" and how it should be "happy Christmas," like this episode's running gag about acronym pedantry.
Journey's End: Timelord reincarnated through plot device and comes back naked.
The Waters of Mars: The Doctor turns up at the start in full tourist mode, then rapidly gets more serious.
Torchwood: Rifts/gates in time; corrupt politicians about to take on more than they can handle with aliens; find-the-Doctor clubs.
Old Skool Who: Deep breath. "Logopolis" (the Doctor meets up with a secret order of aliens who tell him the universe is being disrupted); "The Keeper of Traken" and "The Deadly Assassin" (skull-faced Master); "Meglos" (cactus-headed aliens). "The Talons of Weng Chiang" (partly-formed villain who must consume people to survive). "Inferno" (well-intended large-scale scientific experiment goes hideously awry). "Shada" (villain who turns the whole world into him) plus "The Leisure Hive" (similar, only in that case, the whole clone army turns into the Doctor temporarily). "Image of the Fendahl" (ritual in which the thing being summoned makes itself out of the life energy of believers). The True History of Faction Paradox (plot in which the biodata of a deceased alien is reassembled in a ritual, to bring back said alien, but somehow he comes back wrong) and Kaldor City (mystical being informing protagonist that there are no coincidences; conversation with person invisible to everyone else through the television; dead cult figure who made provisions for his "return", plus see Fendahl above; the homeless charity is called Steven's Point). "The Stones of Blood" (a crypto-lesbian named Mrs Trefusis who's into pagan rituals). "Silver Nemesis" (the ritual, plus an unexpected image of the Doctor's companion in a painting/the Doctor's Tardis in a stained-glass window).
Everything Else: Harry Potter (a secret order determined to resurrect a dead baddie, which they do through a magic ritual; use of magic potions and secret books; a hero reluctant to meet his destiny). Star Wars: Return of the Jedi (lightning bolts from hands fighting), The Phantom Menace (the Time Lords apparently live on Coruscant) and Attack of the Clones (erm... pass). Being John Malkovitch (or, in this case, Being John Simm). Right-wing conspiracy theories about Obama (plausible black politician who's secretly doing some rather evil things). For Your Eyes Only (gratuitous insertion of contemporary, recognisable politician into story, played by an impersonator). The Satanic Rites of Dracula (the ritual to bring back the Master, plus the Doctor-Master relationship parallelling the Van Helsing-Dracula one). Jacob's Ladder (the shaking-head bit). Buffy the Vampire Slayer (character returned from the dead comes back wrong). The Matrix (everybody turning into Agent Smith, plus high-flying martial arts in an urban wasteland). "Stargate". "Ghostwatch" (newsreader possessed by external force). Timothy Dalton's spit-laden speech keeps reminding me of the video for Coolio's "Gangster's Paradise" for some reason. Prisoner Cell Block H, also House of Whipcord (sado-masochistic lesbian prison wardens). Silence of the Lambs (as has been repeatedly pointed out in the media, though they usually just mention the heavy bondage scene and not the fact that the Master eats people). Life on Mars (people sending messages through the television that only one person can see). Battlestar Galactica (armies of identical people aside, there's also a Head Person who appears to one specific character).