Sheogorath's quest where flaming dogs fall from the sky.
During the Thieves' Guild quest "Misdirection", all the guards will run around the Waterfront, asking about the Gray Fox. Sometimes they'll even interrogate each other... and if you're standing nearby, they will look at you and simultaneously ask you the same question. Even better when they have the same voice.
"Rat Ragout with Powdered Deer Penis!"
In Sanguine's shrine quest, he tells you to cast a spell called "Stark Reality" on the Countess of Leyawiin and her company at her dinner party. The spell strips anyone in its range of all of their equipment, but he neglects to mention that the spell also affects the caster (you are completely stripped of all your items when you use it). Using it is also considered assault because it has a "Drain Health 1" effect, so the guards will immediately try to arrest you. So if you don't want to go to prison, (since the spell also removes all your gold so you can't pay the fine) you're forced to run out of the city butt naked with a bunch of angry guards chasing after you.
The stupid random conversation system in Oblivion can result in a lot of hilarity when certain lines are combined.
Citizen 1: "Do you think what happened to Kvatch would happen here?" Citizen 2: "Without a question."*
For those who don't know, Kvatch was overrun by Daedra that spawned from sudden Oblivion hell gates, and then burned and destroyed.
Mage: "Noble scholar, may I have a moment of your time? It's rather urgent." Scholar: "Good day."
Sheogorath, at one point during the Shivering Isles expansion, says, "I'm so happy I could just tear out your intestines and strangle you with them!"
And later - "Then out come the intestines. And I skip rope with them!"
Sheogorath's response if you choose to replace Syl:
SHEOGORATH: A dangerous choice. I like it!
"You have pleased the Mad God! I, for one, would still like to eat your eyes!"
Let's not beat around the bush here, Sheogorath averages a brilliant and usually hilarious line every two minutes or so. At least until his final conversation...
During a certain Mages' Guild quest (Liberation or Apprehension), you meet a Wood Elf named Fithragaer inside an Ayleid ruin (Nenyond Twyll). After a little chat, he eagerly runs deeper into the ruins to beat up some necromancers... and he runs STRAIGHT INTO A CEILING SPIKE TRAP AND GETS KILLED.
To top that there's a glitch that will cause the spike trap to keep activating as long as Fithragaer's corpse is on it. Meaning that the trap will continuously pummel him into the ceiling!
In Skingrad, ask Falanu Hlaalu about the city. She'll ask you if you know what the fine for necrophilia is, and she'll be very happy if you give her the answer.
Protagonist: Is it the first offense? Falanu: Let's assume... no. Protagonist: Then it's at least 500 gold. Falanu: That's nothing compared to Morrowind, thanks!
When you ask Modryn to be second-in-command, he says "I was just getting used to being retired. You can see how good my painting is getting." In the back of his house you can see an example of one of his paintings◊.
If Game Mods count, there's one mod that overhauls the way beggars work (so they can pickpocket you if you stand to close to them, you can contract diseases from them, et cetera) in addition to adding several new ones around the game. One of them, in Skingrad, is a skooma addict and has his own lines. The only thing he'll ever say, no matter what you ask him, is "SKOOMA!". One of your dialogue options? "Aagh, get away from me, you freak!". To which he replies "SKOOMA!"
There's a woman in the Shivering Isles who's addicted to skooma, which she asks you for every time you talk to her. If you give her some, she shouts "Skooma! SKOOMA!"
However, if you don't give her any, she will be greatly upset and tell you she "hopes you trip and fall on a sword!" ...And then give the player a casual "farewell."
In the Shivering Isles expansion, you can encounter Hirrus Clutumnus, who tells you that he wants to end his life. However, he can't actually kill himself, otherwise his spirit will end up trapped on the Hill of Suicides, so naturally he asks you to do it. Fortunately, he happens to visit a balcony without railings, and you have the dialogue option of pushing him off. The best part is the total non-reaction of the Dark Seducer who sees the whole thing happen. Apparently this sort of thing happens all the time...
One cavern unrelated to any quests features a dead goblin and a large beer keg. The goblin is lying on its back with its face under the spigot.
One quest is given to you by a drunk who believes that there's someone in Cheydinhal that looks like him. He tells you, dead serious:
Reynald Jemane: You're going to travel to Cheydinhal, and find out what sort of imposter is trying to besmirch my good name. And you're going to tell him... *hic*... You're going to tell him I am quite capable of besmirching my good name on my own. He should cease and desist immediately.
The Summon Haskill power from Shivering Isles. Haskill is Sheogorath's chamberlain and literally the Only Sane Man in the entire realm. If you haven't played the game, imagine you have the power to summon a stereotypical dry-witted British butler at will to give you helpful but snarky advice on your quests.
There's a dungeon in the Shivering Isles specifically designed to lure in adventurers and screw with them. The one that takes the cake is an illusion that makes an orc see his corpse laying on the floor and see himself as a ghost. He has a debate with himself about how he can't possibly be dead because he wasn't in a fight yet there's his body and its so unfair.
Imperial Legion Foresters are programmed to hunt deer. Deer are programmed to be friendly to foresters, so if the forester sees anyone else attack a deer, they'll start fighting the person. Sometimes, the foresters' patrol areas overlap, and you may come upon a scene like this...
Even better, if you're playing as a lawful character, when the forester manages to kill the other forester, he can turn to you and say "It's nice to see a friendly face in these dark times"
You finally get the chance to make the arrogant Yellow Team Champion in the Arena eat her words late in the questline. However, it's a three-against-one match. The Arena Blademaster decides to even the odds a little in your favor, though, by sending a boar named Porkchop up to have your back!