Farnham, the drunken guy (who is about useless otherwise), when asked about the Poisoned Well quest: "You drink WATER?"
The premise behind the Inn Sign quest is rather amusing. Basically, a band of Fallen led by Snotspill steal Ogden's sign, which is a rising sun, thinking it was magic, and carry it off to the cathedral basement. During that time, a group of Overlords steal it from THEM and are keeping it for themselves. You are tasked to retrieve it, and are given an option. Return it to Ogden, who basically shrugs, but rewards you for saving him from having to get another sign made by giving you the Harlequin Crest; or return it to the Fallen, who makes a great hammy speech and cackles maniacally, as if you'd just granted him a legendary artifact of uncomparable power. Either way, however, the humor ends with the incensed Fallen zerg rushing you.
The Black Mushroom quest. After presenting the Fungal Tome to Adria, you are tasked with finding a big, Black Mushroom for use in an elixir. The villagers' reactions are best described as perplexed and exasperated; uncharacteristically, Ogden (who is normally very mild-mannered) is thoroughly offended. Upon finding the mushroom patch, your character will react with surprise at just how large the mushroom really is.
If you find out what Diablo is really saying the instant the final level starts...
And of course in the first game's Hellfire expansion, through a certain exploit, you get to hear Na-Krul say this gem.
Na-Krul: Hi! I'm free, free to confront the little man who banished me, Diablo. Hi, everybody, and I'm free to reward you, little mortal, with these Aerosmith tickets. You'll be getting backstage passes, you'll get to meet Steven Tyler and the whole band. This Friday at the Coliseum. Thanks for getting me out of there. By the way, I'm gonna have to kill you. *pause* I'll be right back with the traffic and weather together.
Also available in the Hellfire expansion was the ability to replace said farmer with the "Complete Nut", a man wearing a cow suit, who sends you looking for his other suit (not the brown one, the gray one) that turns him into a man wearing a deer suit, and awards you with the Cow Plate Armor.
Moo. I said 'Moo'. Listen, I'm just a cow.
One of the cited reasons for why David Brevik hates and ultimately disowned the Hellfire expansion? "It has a fucking teddy bear quest."
In the Swedish dub of the PSX version, if you keep on trying to talk to a cow you can end up with quite the funny line "Jag är ingen mjölk-kärring.", roughly translating to "I am no milk hag". The deadpan and mildly annoyed delivery is what truly sells it.
