The entirety of Foolhardy Waywardness. Sir Christian, an aspiring "Fragrance Alchemist", is marooned on an island with a bunch of dimwitted natives and has to jump through ridiculous hoops to get some semblance of help from them. This includes building a capitol on a dung heap, being thrown onto a dinghy and tossed out to sea, being kidnapped by pirates, and finally as he is rescued, he gets dragged into the Restoration War. Oh and the Forks. All of the Forks.
During the Armageddon's Blade campaign, Xeron finds out that Gelu has killed the former's mother and is in total anguish. When we play as Gelu, we find out that the only woman he could think of killing was a succubus trying to steal his soul, and she was apparently so terrifying he couldn't imagine her being the mother to anyone.
Part of the Elixir of Life campaign tasks you with stealing the Vial of Lifeblood from Vokial, a vampire who's using it to avoid having to feed off living creatures. Lord Falorel justifies this because it would embarrass Vokial, which is hilariously childish. With the later revelation that Lord Falorel was himself a vampire, it honestly seems like this whole mission was him sending Gelu to pull a prank on his buddy.
Crag Hack. Not only does he speak in stereotypical barbarian Hulk Speak, his interactions with Sandro are pretty funny, with Sandro constantly calling him "Mr. Hack" and Crag wearily correcting him every time. One has to wonder if Sandro starts doing it intentionally because dealing with Crag annoys him.
The sheer Culture Clash Tarnum goes through in Masters of the Elements, as he is forced by the Ancestors to be a Wizard. Especially early on.
One event in the first scenario is the request from mages working with Tarnum - to let them build a Mage Guild, likely echoing the players' thoughts as the player is not allowed to build one. Tarnum is not moved.
Heroes of Might and Magic V
Markal, despite being a Smug Snake extraordinaire, can be wonderfully sardonic:
[Markal stands surrounded by the smashed up corpses of his defeated army, as Godric, Findan and Zehir approach him]
In the Inferno campaign, if you wait long enough during the battle where you play as Azkaal, a baseball will come flying towards Azkaal and he'll bat it away with his giant sword as his idle animation.
Everything Bluebeak says in her dialogue. For a bird that can only squawk, she is surprisingly witty.
The same goes for Daeva. The fact that she's a Succubus makes it even more funnier.