A phrase I don't think I've seen in any book yet.

[Doctor X]

I expected to see it somewhere in the 5th through 7th Doctor sourcebooks, but did not. (6 especially, as I seem to recall it being said more than once in his stories.)

The Ends Justify The Means

This is the primary motivation behind almost every Doctor Who villain who isn't one of the major recurring foes. (And even amongst THEM, it's the Rani's motto.) It's certainly what drives most of the mad scientists and pig-headed military types that the Doctor encounters. And it's something to keep in mind to help GMs come up with their own stories: This will be what motivates your villain.

Unless you're a Dalek, you don't just wake up in the morning and say "Today, I'm going to create a virus that kills half the planet just because I can." There's a reason you think the world needs your population-reducing virus. (The world is too crowded, it's "the only way to end this war," the ones that survive will bow to my genius and I shall lead them into a new Utopia.)

Once you have that as the NPC's core belief, you can ask yourself "What ends and what means are we talking about," and you've already begun writing your adventure.

[Catsmate]

Well AITAS devotes only half a page to antagonists and their motivations while it's a far more complex subject. Then again Who is often bad at giving antagonists/villains realistic or at least plausible motivations.
The Ends Justify The Means is a good over-riding principle but it usually needs more detail, what are the ends and the mean justified?


Wealth
In Who this is generally for the small fry, mere wealth or good don't interest the major players.
That said money can be a means to an end, i.e. Scaroth financing his experiments in time travel using Mona Lisa copies, or resources might be urgently needed (like parranium to produce a plague cure). Or a desire to gather a collection of some sort, objets d'art perhaps.


Power
Pretty much the classic motivation for Who villains.
Can be combined with building a better world, wouldn't everything be so much better if the Think Tank were in charge?


Survival
Even at the pricer of others not surviving, e.g. the Silurians wanting 'their' planet back


Ego/acknowledgment.
A villain who wants to win to demonstrate his own superiority or gain the approval of someone (or a group) whose respect he wants.


Personal amusement.
Mischief or worse. An old time travel game I was part of (not Who based) had a minor recurring character named Adam, a charming, low profile independent time traveller who was a sadistic psychopath. However he was simply too insignificant a threat to causality, and potentially too dangerous to engage, that he was difficult to stop. The film Time After Time and the TV series Lois and Clark both featured a time travelling Jack the Ripper.


Curiosity.
One motivation I've used for time travellers is simply to find out what would happen if they changed a past event; kill Hitler (to choose a trope) and them examine the changes that propagate forwards.


Revenge
A pretty common motivation for the Master who'd frequently create elaborate traps to capture/kill/humiliate the Doctor.


To Build a Better World.
Or universe of course. Wouldn't the world be a better place if event X hadn't happened, or group Y didn't exist? A common motivation for anti-heroes who might argue that starting one war might well prevent a far worse one or utterly destroying the present to make way for a better world (Invasion of the Dinosaurs).
Adrian Veidt (Watchmen) is  classic example of this, believing his end justifies the means he uses.


Chaos.
To spread disorder and destruction. This seems to be the motivation of the Daleks, some of the time anyway.

[Marnal]

My notes on What Makes a Good Doctor Who Villain...

Major Antagonist / Villain: The Villain is out of balance & a genuine threat. Villains can be multilayered.

1. An extreme "I am the World" (Eastern) POV - "The rest of the world does not matter"

2. Or an extreme "The World Belongs to Me" (Western) POV - "Understanding and Control of the World is the only thing that matters".
--a. Megalomaniacs are common. They believe they have a destiny.
--b. These Villains define themselves by the ability to influence and control the world around them. “I WILL therefore I am.”

3. Human villains should have their baser instincts getting out of control.
--a. Aggression: Must destroy the problem
--b. Profit: Progress and money is everything.
--c. Hubris: I must learn and control the secrets of the Universe!
--d. Tradition: Must ensure the Old Ways continue.

4. The Villain isn't always the cause/creator of the problem. The villain might be trying to exploit the problem or the mystery.