Rose: Companion bids farewell to Doctor; Tardis flies off; then is back two seconds later.
The End of the World: "She's/he's my plus-one." Old human resorting to science to stay young/alive.
Aliens of London: Rose returns after twelve months in the company of a mysterious older man called the Doctor, and Rose's mum excoriates him, slaps him, urges Rose to have nothing to do with him and shops him to the government. Martha's mum does exactly the same, although, since Martha's only been away twelve hours, David Tennant doesn't look older than about thirty, and Martha, being a medical student, has a reason to be hanging around doctors, it's a bit more of a baffling response in the case of Mrs Jones. And the government shops the Doctor to Martha's Mum, but that's an inversion rather than an outright change. Human transforming into improbably larger monster and hunting people.
Dalek: Monster goes on rampage, building complex goes into emergency lockdown, cue scenes of people panicking along corridors and up staircases as they try to escape it.
The Long Game: Tardis lands in living room, next to a phone with an answering machine which turns out to be somewhat significant to the story. Emaciated, drained corpses.
The Empty Child: "That'd be the Blitz."
New Earth: Everything has its time; old people should accept death and not go all mad trying to fight it; the Doctor feels a bit depressed at his own longevity.
School Reunion: Monster jumping around ceilings and walls (it even looks a bit like a giant Krillitane); monster in human form cricking its neck to indicate that it has just reverted; authority figures being really human-eating monsters.
Rise of the Cybermen: Companion and Doctor go to party; Doctor dresses in tuxedo while companion chats up her relatives; party suddenly interrupted by glassware-smashing monster.
Army of Ghosts/Doomsday: The Doctor gives his companion his sonic screwdriver and tells her how to use it as a sign that he trusts her; power failure causes unstable creation of monster (Yvonne Cyberman there, the Lazarus monster here); the humans in the story take for granted an occurrence which the Doctor finds very suspicious.
The Runaway Bride: Spiderlike monster with human face and with plans for world domination. One character distracts the monster from attacking another one.
And, guess what, they're even recycling this season...
Evolution of the Daleks: Mentally unstable human hybrid monster that is affected by sound; really old-fashioned labs with glassware and coloured fluids (incurring sequence of Doctor lighting bunsen burners/gas taps); a plan to "change what it means to be human" going rather awry.
Timelash Moment: False ending where it looks like the monster/villain is dead... and then, surprise, it isn't.
The Fifth Element: Dodgy businessperson comes to sticky end after backing dubious project.
Old Skool Who: Ripping off Nigel Kneale is a time-honoured pastime, particularly if you're Robert Holmes-- precedents include The Ark in Space, The Seeds of Doom, and others; the scientist-with-invention-that-goes-horribly-wrong is another Old Skool staple (precedents include Robot, The Talons of Weng Chiang, The Mind of Evil, The Two Doctors, Genesis of the Daleks etc.) in "Vengeance on Varos" people "devolve" into unlikely creatures; The Invasion of Time again (monster affected by sound); The Leisure Hive (treatment purported to rejuvenate the old, which goes wrong); the dessicated corpses look like the ones seen in Planet of Evil and The Horns of Nimon, for the same reason in all cases.
Everything Else: The Quatermass Experiment (human hybrid monster up a cathedral being talked down; apparently in the original script it was St Paul's, which would just have made it even more of a ripoff); The Fly (scientist experiments on himself in big glossy chamber and having it go horribly wrong); Life Force (monster draining people of their life energy; this story also ripped off the Quatermass serials shamelessly); Star Trek: TNG: "Genesis" (people "devolving" back into animals; the science is a bit differently explained but just as improbable); Carpenter's The Thing (creature with human face); Lost In Space the 1990s movie (where poor old Gary Oldman gets CGI'd into a kind of spider/scorpion creature with a distorted and spiky version of his face; I'll just remind you that RTD says in the Confidential that he "wanted a really original sort of monster"); Predator (the way the creature opens its bottom jaw); Spider-Man 2, apparently (I've more or less forgotten the whole movie, myself, but apparently the botched-transformation scene is ripped off from something Doc Oc did); the New Testament (with a surname like Lazarus, you just know there's going to be rising-from-the-dead hijinx); Cold Lazarus by Dennis Potter (not just the name, but also a dodgy older woman who really, really wants to become young again backing scientific research with dubious implications).