This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / Faction Paradox
The Faction Paradox. They have their roots in corrupt Gallifreyans worshipping paradox and defiling history and glorifying death as the mother of all Take Thats to the Time Lords. They entered existence by paradoxically creating their own creator. Said creator became a monstrous undead paradox being whose shape depends upon who's looking at him. The shape he always uses? A twisted image of the viewer, being "everything you swore you'd never be". In essence, the embodiment of all potential evil in the universe. The Faction as a whole has as a favorite sport for initiates a manhunt in which they are led to their ancestors and Unperson themselves by murdering dear old papa or gramma before they themselves are born, therefore erasing themselves out of history and making them harder to destroy by time-based attacks. They wear masks of pure bone out of the skulls of creatures that never ever existed. They use huge skeletons as warships. They merge weapons with their shadows and turn them into living monstrosities that can slice apart rooms while the priest remains calmly sitting.
A particular member of the Faction mentioned he once murdered his father. Typical. And then went to his timeship and went a few hours earlier. And killed him again. And again. And again.
The Celestis are the former Celestial Intervention Agency agents, who feared that in the War they would be erased from history. So they did it to themselves in their own terms. Now, a moment to think... a lot of members of a society where paranoia and Chronic Backstabbing Disorder is the norm, turned into Energy Beings, who can only remain anchored in reality as long as someone believes in them. The A God Am I scenario, predictably, is the best of all. As a commenter states on their rotting society: nothing can be all right in a society where everybody is either a god, a slave or an assassin.
The Yssgaroth, infinitely horrific monsters from another Universe, are related to the Great Vampires of the normal Whoniverse, so you know it's going to get bad. Their taint is easily transmissible and the timeline in their universe is implied to be self-cannibalizing. Turns out, they're grand at the biological scientist thing. How good are they? Good enough to string your nervous system across continents while leaving you fully conscious, incapable of death and of feeling anything other than endless pain. Fate Worse Than Death doesn't begin to describe what will happen if the Yssgaroth get you. Oh, and did we mention there's a good possibility the Yssgaroth are all part of a single, unfathomably huge organism? And the local Time Lord expies have been leading incursions into their universe for military purposes?
The Eleven-Day Empire. An extradimensional realm created by mutilating Earth's history and populating it with Eldritch Abominations by the goddamn truckload. It is protected by entities implied to be the physical embodiments of the Laws of the Universe. And the massive potential for Temporal Paradoxes merely by existing there for any length of time. And then came the news of the War in Heaven...
The War in Heaven. Imagine you have access to a time machine. You are engaged in combat with another person who also has a time machine. A wreckage of a Gambit Pileup later, none of you are closer to killing the other as both continually fight to retain your timeline intact even as you try to make Time itself your bitch as you alter time as well as you can with your technology. Now, placed in perspective: imagine it's not two, but trillions of participants in a battle royale for control of the Universe in every moment in time. Now you perhaps understand. And there are people seeking to exploit it! The gall of them! But do not worry, friends. The Faction's door is always open...
The true Homeworld of the Enemy has been identified in Interference- it is none other than Earth!
The Time Lord Invasion of the bottle universe Earth in Dead Romance.
Serviceman Sabbath in "Sabbath Dei" cuts himself open to summon a "presence." What's really creepy is the cold, clinical tone in which he discusses his injuries. He seems perfectly aware that what he's doing is insane yet he keeps doing it anyway. It's a bizarre combination of sanity and insanity.
The Shifts, living memes who exist in the memetic connections between a written work and its viewers.
The victims of the Timebeast Assault, in which the Homeworld released several timeship-wyrms into the City Of The Saved and had them eat the Citizens alive. The City built new copies of the victims afterwards. The original resurrectees are still out there... somewhere.