Sutekh, Last of the Osirans, from "Pyramids of Mars". At the time, the Doctor describes him as the worst threat he has ever faced, the greatest time of peril in the history of the Earth, and given his awakening would have rendered the planet a barren wasteland before he spread across the universe to kill everything, his concern was very much justified.
The eponymous creature in "Image of the Fendahl"; everyone who saw it died of fright, and that was only a crippled ghost of its true self 12 million years dead, which had been manipulating human lineages for millennia to ensure its release. In the Doctor Who Expanded Universe, the Time Lords deliberately created a predator capable of feeding off the Fendahl - the Memeovore, or Devourer of Concept, a malign void which could reach across time and space to feed on the stuff of thought and hungered to devour all eternity, from the Big Bang to the end of time. Those who looked at it saw an endless procession of grotesque images, as their mind struggled to comprehend the incomprehensible. And then the Time Lords released it to use for warfare.
Not everyone who saw the Fendahl was lucky enough to die of fright. The Core transformed some of them into Fendahleen (the other components that, together with the Core, make up the Fendahl). The leader of the cultists who completed the process of creating the Core had worse luck than that. He was still alive, still human, and seeming still sane... but what he saw when he looked into the eyes of the Fendahl caused him to request the means to kill himself. How bad it was is evidenced by the Doctor giving him those means.
The Great Vampires, who fought the early Time Lords in the war that made the entire species get sick of violence, are gargantuan winged creatures who feast on planets, and can only be killed by having their heart destroyed. But they are so massive that the Time Lords had to invent a new type of ship specifically for hunting them. The only way the Doctor managed to best the one he encountered was by stabbing it with a rocket ship.
The eponymous Big Bad in "The Curse of Fenric" is described as evil incarnate from almost the beginning of the universe, albeit one without a body of its own, instead possessing others' bodies. One of the spinoff novels identifies Fenric as Hastur the Unspeakable from the Cthulhu Mythos.
The Reapers from "Father's Day" may be an understated example, but they're still incredibly terrifying winged beings that are literally linked to "Time" itself and appear whenever a Temporal Paradox happens like "bacteria taking advantage of the wound". It gets even worse when the Ninth states the only things that could stop them are appropriately enough the Time Lords but since they're out of the picture (heh) the Reapers are unstoppable and will devour everything until the paradox is fixed. The Reapers are one of the very few foes that can deactivate the Tardis and in the Four Doctors comic a Reaper smashes straight though the Tardis like it's made of... well, wood.
In Torchwood, we meet its spawn, who kills people with its shadow. An Expanded Universe novel reveals that it is actually keeping even worse beings at bay, and that it killing people for the energy required to do so is simply "collateral damage".
The... creature from "Midnight". We don't see much of it, so it's nothing definite. But it Mind Rapesthe Doctor and, by turning the people he's trying to save against him, comes closer to killing him than anything else.
Sky/Doctor: He's waited so long. In the dark. And the cold. And the diamonds. Until you came. Bodies so hot. With blood. And pain.
Even worse, the Doctor has no knowledge of the creature. He doesn't know where it came from, how long it was there, what it is, if it's the only one of its kind in the universe, or how to beat it. It's one of the very few times in the entire decades long history of the show that something like this has utterly stumped and terrified The Doctor. The Hostess ultimately sacrifices herself to push the Possessed Sky out of the carriage. The Doctor remains shaken, and says the planet should be left alone, suggesting that either he doesn't believe it's dead, or he believes there's more than one of them.
The Doctor: Let this planet keep on turning around an xtonic star. In silence.
The Old God, or "Grandfather", from "The Rings of Akhaten". A creature so powerful even the Doctor is willing to consider it a god, which has been sung to for millennia (constantly, with singers rotating in and out but the song never having been interrupted, ever) because if the songs cease for even a second, it will wake and devour all existence (oh, and it's the size of a planet). The parallels to Azathoth couldn't be more blatant.
The Moment is one of the more understated ones, and yet probably the most powerful in the series. Never mind that it's a weapon with the ability to destroy worlds, and a piece of mechanics complex enough to develop a conscience; throughout its only appearance it repeatedly and calmly punches holes in the Time Lock around the Time War. As a reminder, this is the same barrier that's strong enough to (mostly) seamlessly contain the full might of the Daleks, Time Lords, and every other Eldritch Abomination they brought with them. For her part, she spends her time convincing her users not to employ her for her designed purpose of immense destruction because she finds the whole idea just terrible.
There's a lot of evidence pointing towards the Time Lords being an entire species of this trope, given their incredible age and intelligence, how easily and often the very laws of reality are twisted like playthings by them (in Classic Who, they are easily capable of moving entire planets and monitor all the energy in the universe), and their inherent ability to perceive the universe in ways no other species can. Indeed, several of the conflicts between the Doctor and the Master play out a lot like battles in an endless war between two Eldritch Abominations, with the poor lesser beings caught between.
In the Expanded Universe, fighting a war even worse than the one described in the TV show, Time Lords are combat bio-engineered to regenerate into the perfect soldier for any environment. In one case, this means turning into minor Cthulhu Mythos creatures. One becomes nothing less than a sentient timeline.
Remember the Doctor's line from "The Pandorica Opens" about the thing the Pandorica was designed to hold: "There was a goblin, or a trickster... or a warrior... A nameless, terrible thing, soaked in the blood of a billion galaxies. The most feared being in all the cosmos. And nothing could stop it or hold it, or reason with it. One day it would just drop out of the sky and tear down your world." It's the Doctor himself.
An assortment of Eldritch Abominations apparently rose from the midst of the Last Great Time War, such as the Nightmare Child, the Horde of Travesties, and the Couldhavebeen King with his armies of Meanwhiles and Never-weres. The Time Lock around the War is there, in part, to stop these things from ever getting out.
The Eternals, beings that live outside of time in eternity, are immortal and use the imagination of people from our universe (they call us Ephemerals) to form realities. They can take anyone they want from any point in time and force them to do whatever they wish. They are not invincible, though; if somehow trapped in our reality, they are mortal and vulnerable.
Again from the Expanded Universe, the Ancient Old Ones, beings from the previous universe that follow different physics, which allows them vast Reality Warper abilities; this can be inverted with beings from the next universe that have similar powers.
The Nestene Consciousness, a formless entity powerful enough to control innumerable psychic links over many light years, capable of bringing life to any plastic which it uses to launch an invasion army. In the Doctor Who Expanded Universe it's one of the thousand children of Shub-Niggurath.
The Weeping Angels: impossibly fast creatures, indistinguishable from ordinary statues until you look away, able to transport people through time (because it's how they feed, off of all the "stolen moments"), and reproduce by projecting themselves through images, including images inside a person's mind. On top of that, if they have enough power, they can turn ordinary statues into more of their number.
In the spinoff Class, it's revealed the Angels are working with a group of humans preparing for an "arrival" involving what appears to be some sort of super-Angel, or Angel god, which seems to be even worse than the usual kind.
The Great Intelligence, a powerful, disembodied consciousness that whispers in people's minds for years or even decades to turn them into willing puppets, and was infrequently encountered until "The Name of the Doctor" — in which it makes an almost successful attempt to destroy the Doctor's entire life back to even before he ever left Gallifrey. Before that, it attempted to steal all of the Doctor's life experiences and memories and mentally revert him back to a younger age. It manifested bizarre powers and whenever it deigned to take physical form, it could Body Surf if the body it was in was damaged. The Doctor Who Expanded Universe identifies the Great Intelligence as an alias of Yog-Sothoth.
Borusa and the other Time Lords Rassilon experimented on in "Engines of War". Their timelines have been retro-engineered, meaning they are in a constant state of flux between the past and possible future regenerations. They can see all possible timelines and when Borusa is in the Eye of Tantalus he is able to pull on threads of possibility to bring new timelines into being; similar to Bad Wolf he is able to wipe all traces of the Daleks from the Tantalus Eye.
The TARDIS itself is a fully sentientEldritch Location.Bigger on the Inside, filled with endless wonder and terror and secrets the Doctor doesn't let even his closest friends in on, able to go anywhere in time and space - and very much alive and in more control of its movements and every single square centimeter of its as-big-as-it-wants-to-be interior than whoever is at the wheel. When a salvage crew captured it and tried to remove parts, we find out what it means to make the supreme mistake of pissing her off. Basically... don't.
Eleventh Doctor: "Don't touch a thing. The TARDIS will get huffy if you mess."
The Doctor Who Expanded Universe says the TARDIS is a full-on Eldritch Abomination, which considerately disguises itself to avoid reducing the passengers to gibbering wrecks. As a living shape-shifting creature, at home in extra-dimensional spaces, with a mind even the Doctor deems unfathomably alien, it's certainly a good candidate. A minor story comments on the TARDIS' mind as completely and utterly pandimensional.
Big Finish Doctor Who: Anti-Time essentially causes this. It is spread by the Neverpeople, people who have experienced Ret Gone, and are left as ghosts who devour people's time. Then there is the personification of Anti-Time, Zagreus, something which even Death fears:
Zagreus seeks the hero's ship Zagreus needs the web to rip Zagreus sups time at a drip And life aside, he's sweeping.
The monsters imprisoned in the Axis of Insanity, a collection of doomed, collapsing timelines, from the Big Finish audio of the same name. The Keeper of the Axis hates the Time Lords, mostly because it's their meddling that made the Axis necessary in the first place and which keeps adding more broken timelines to it.
"Ancient lights", Hive Queens to at least part of the universe that existed before the Big Bang. They are capable of using astrology to brainwash others and give them tremendous powers because the universe they originated from used astrology as a science. The fact that the physics of the current universe does not work according to those rules does not matter, they can ignore that and use it regardless.
The Trickster, part of a Pantheon, whose sole motivation is to cause chaos in the universe at large. He can alter the timeline at a whim and create an entire parallel universe as long as he has the agreement of someone and he can feed on the chaos that change has.