The ancestral tombs. It's not enough that they're all cramped dungeons, but then you hear the ancestral spirits whisper. Then you find yourself brutally surprised by one of the various permanently grinning undead.
Dagoth Ur is literally nightmare fuel, he is a Mad Dreamer who gives Bad Dreams to people. Here's a quick example: note I AM THE SHARMAT I AM OLDER THAN MUSIC WHAT I BRING IS LIGHT WHAT I BRING IS A STAR WHAT I BRING IS AN ANCIENT SEA WHEN YOU SLEEP YOU SEE ME DANCING AT THE CORE IT IS NOT A BLIGHT IT IS MY HOUSE I PUT A STAR INTO THE WORLD'S MOUTH TO MURDER IT TEAR DOWN THE PYLONS MY BLIND FISH SWIM IN THE NEW PHLOGISTON TEAR DOWN THE PYLONS MY DEAF MOONS SING AND BURN AND ORBIT ME I AM OLDER THAN MUSIC WHAT I BRING IS LIGHT WHAT I BRING IS A STAR WHAT I BRING IS AN ANCIENT SEA
Corprus disease is And I Must Scream in a contagious form. It's similar to leprosy or cancer... but worse. Corprus twists your mind and body the longer you have it, sapping your intelligence and driving you mad. Like leprosy, it is obvious and causes almost everyone to wish that you'd go away. You will eventually become a shambling, tumorous mass as the disease takes effect; the perpetual agony will leave you Always Chaotic Evil, lashing out mindlessly at anything that comes near - and potentially spreading the disease to them. It also stops the aging process, so if you catch it and don't die of it, you'll live until somebody kills you. And you won't have the mental faculties to commit suicide any more. All you will know is the pain - and the will of Dagoth Ur. There is no known cure.
If Dagoth Ur wants you as a minion, your case of corprus will become more benign: you will still mutate, but not into a tumorous blob of flesh. Instead, your eyes will wither and disappear, your skin will become covered with ash, your brain will atrophy and the entire upper half of your face will collapse to uncover your empty skull, and, finally, a trunk-like tentacle will grow out of the hollow to replace your brain. Eventually, the tentacle growth will branch into a writhing mass, turning you into a cthulhumanoid. Your sentience will return to you when you get the tentacle-brain, as will your well-being... but you will become a minion of Dagoth Ur forever.
You can use soul trap on Corprus and Ash creatures, meaning Dagoth Ur's plague not only warps your body, but also turns your soul white, viable for soul trap.
A very long-term one, but the knowledge that Morrowind is destroyed by the actions of the Nerevarine. When the rogue moon falls on Vivec and sets off a massive eruption at Red Mountain every major settlement on Vvardenfell is leveled and many mainland cities are also destroyed. The death toll is in the millions and it's all your fault, congratulations.
The alternative would have been to allow Dagoth Ur's consciousness to take over that of every single other living being there is, eventually coming to engulf the universe in its entirety. That's not horrifying.
The absolutely benign third option, namely, giving the Tools to the Tribunal and allowing them to restore their strength at the Heart while kicking major ass of Dagoth Ur and his ash vampires, would lead to the restoration of ALMSIVI to their glory days and giving Morrowind another 1000 years or so of calm. But it is, sadly, not implemented in the game, because Azura does not want you to do this.
Considering that Almalexia starts killing other gods, this may not be a good end.
Her crazy murder cravings are a direct result of losing the Heart, having only the faith of the people as a source of power and not wanting to divvy this meager source in three parts. Having the Heart back will make her revert to her old nice self.
Also, the Dunmer are notoriously xenophobic and the only society in the setting still insisting on a right to keep slaves. In fact, one off-screen House uses mass slavery on plantations to provide basic food security for this whole society (salt rice), and they regularly go on raids into the territories of two other races to enslave more people. Another House is all about national pride and martial prowess. Another is made up of religious fanatics. Would it really be a good thing to give them a chance at maintaining this system for another 1000 years and potentially manage enough internal stability to attack the Empire in revenge once it is weakened by the Oblivion crisis?
This option also isn't possible. The Tribunal losing the Tools to Dagoth Ur and his Ash-Vampires only happened 10 years before the game started, in 3E 417. This outcome dramatically worsened their position and hastened things to the crisis point they find themselves in when you step ashore in Seyda Neen, but the fact of the matter was that they were already explicitly losing against Dagoth Ur, even with the Tools of Kagrenac. Dagoth Ur straight up beat them at the height of their power when he ambushed them in 2E 882. They have no ability to defeat him- it can be inferred, given that they only lost the Tools 10 years before, but have been attempting the plan they gave to the Nerevarine for 20, that the Tribunal had already realized it was their only realistic plan.
In one cave, you can find several dead bodies, skeletons and a potion ingredient: human flesh. Squick.
The ash creatures. They are all creepy, but the fact that they all used to be human (well, Dunmer) as well just pushes it beyond creepy and full-on into horror. To get into the juicy details...
You have the aforementioned Corprus sufferers, with Stalkers possessing rotting skin and various cysts; while the more mutated Lame Corprus are in full-on Body Horror, with the flesh around head and half of their body is swelling grotesquely to the point where it looks like their flesh is actually tearing through their skin! And their faces...
Ash Slaves are the least mutated... by which means that their emaciated bodies have taken on an ashen pallor while their eyes have shrunken to the point where they don't look like they even have eyes.
Ash Zombies are further down the valley, with the top half of their skulls completely hallowed out and leaving them without eyes, a nose, and a brain. Despite this, they're still intelligent and are without mercy.
Ash Ghouls may now wear proper clothing, but they still bring the horror with their faces. Unlike their lesser Zombie brethren, Ash Ghouls have a wormlike proboscis growing out of where the Zombie's skull cavity is. On top of that, they're even more intelligent, to the point of sentient... if only to continue their fanatical mission for Dagoth Ur.
And finally the Ascended Sleepers, pictured above. Physically no longer human, and now just Eldritch Abominations with a quartet of hollow-looking eye sockets and tentacles growing where their faces should be. They're the most powerful and dangerous of Dagoth Ur's minions.
The castle Tel Vos. Normally, it's not that creepy, but when you explore the depths you find that it's (almost) entirely abandoned and overrun with giant plants. The part that drives it home is how you keep finding diary entries from those who worked in the castle as everything went to hell. And the owner and his servants nonchalantly live on the upper levels like there's nothing wrong.
Morrowind's dungeons often contain Daedric shrines, which invariably have offerings laid out in front of them. These are always valuable objects, precious stones, weapons and such. But there is a catch: the Daedra to whom the shrine belongs views those objects as its own, and evidently does not take kindly to you thieving them. One of the offerings - just one - will, if you touch it, immediately summon something very nasty behind you.
A similar example happens in a Dunmer ancestral tomb. When exploring such tombs, at times you will come across an intact skeleton, laid to rest. Nothing unusual, these are tombs, after all. In one such tomb however, after picking some loot, one of the skeletons is awakened and attacks you. It's a little unsettling in that the skeleton is in a different room when this happens, so you'll be treated to the combat music without an enemy in sight, only to walk out of the room and find that the skeleton you just walked past has been reanimated.
The in-game book Chance's Folly. The insane warrior's betrayal of the young thief is quite disturbing, as she is sealed for the rest of her life in a room with no way out. And to top it off? It's not fiction, either. Try dropping in to one of the ancestral tombs in Morrowind...
Another freaky in-game book is the innocently titled Surfeit of Thieves. In it, a pair of thieves, a male named Indyk and a female named Heriah, find a secluded castle. Told by others it is full of riches, but occupied by monks, they plan to break in. With Indyk apparently distracting the guard, Heriah breaks in elsewhere. She gets caught by one of the occupants of the castle, who asks her if she is "Lady Tressed". Going along with the deception, she allows the monk who caught her to lead her back to a feast, where her partner is sitting at a table, albeit hooded to disguise himself. At the table, she notices, during the introductions from the monks, that all their names are backwards, due to an enchantment set to run out after the hourglass at the center of the table does. At some point, she hears her partner be referred to as "Esruoc Tsrif", shortly before trying to leave. However, the monks stop her from leaving, just as the enchantment runs out. If you don't understand why this story is freaky, look at the names the monks gave the thieves, and remember that the enchantment makes stated names backwards from the true names...
The Sixth House bases are generally pretty dark and creepy; first take the ash creatures previously mentioned, then add things like those giant voodoo doll looking things, bells that are capable of producing near-BrownNotes, and at least one of them features bizarre furniture arrangements that brings to mind Poltergeist.
The hulking Grahl enemies found in the same dungeons have the opposite effect but can be equally dreadful. When you first run into one you usually only see a pair of glowing red eyes and a giant, vague silhouette as it slowly walks closer to you.
Netches. Though there are many odd enemies in Morrowind you can count on most of them being humanoid and ground-bound. Then you find a pack of these slow, physics defying, impossibleeldritch abominations. If you're brave enough to approach and hit one it will instantly flail around with sudden and unnerving speed, battering you with its foreign tendrils... All the while more of these cosmic horrors approach and begin to surround you.
At the start of the final quest in the Bloodmoon expansion, there will be a nasty Jump Scare when you wake up and see multiple werewolves surrounding your bed as you are taken to the lair of Hircine.