Lord Vetinari, dictator of Ankh-Morpork, juggling and shilling a game of guess-which-cup-the-egg-is-under. Later revealing that he actually never learned to juggle, and he always knows where the chicken is.
The few times that Vetinari is ever caught off-guard.
Any time that Vetinari finds something amusing is also usually pretty epic.
Vimes' internal monologue when he talks about investigating the attempted assassination of Prince Khufurah, and wonders who of the Ankh-Morpork bigwigs at the table might be behind it:
"I'm putting my best men on the case". Who's looking worried? "Sergeant Colon and Corporal Nobbs." Who's looking relieved?
Leonard of Quirm offhandedly makes a comment quite pertinent to the story, and Vetinari makes it halfway back through his elaborate trap system after leaving the room before it registers. He then comes back as quickly as possible, straightens himself out, comes in, sits calmly down and says, "You did WHAT?!"
Nobby's crossdressing act, when the narrator points out the complete and utter aversion of the Attractive Bent-Gender trope, because this is Nobby Nobbs we're talking about, and it gets even better when Nobby turns into an exaggerated caricature off a Straw Feminist and has to be constantly reminded that he is not, in fact, a woman.
Corporal Nobbs's appearance could best be summarized this way. One of the minor laws of the narrative universe is that any homely featured man who has, for some reason, to disguise himself as a woman will apparently become attractive to some otherwise perfectly sane men with, as the ancient scrolls say, hilarious results. In this case the laws were fighting against the fact of Corporal Nobby Nobbs, and gave up.
For added hilarity, Nobby soon realised that he could utilize his newly obtained feminine wiles to obtain food and a fully functioning flying carpet from the enemy force — i.e. he told the Klatchian quarter master that he would take off his clothes and scream, unless given food.
"I've only been a woman ten minutes and already I hate you male bastards."
Lord Vetinari, under arrest for treason, asks if it's possible to be dragged through the streets in chains on a hurdle. Nobby reports from the sports shop that they don't have hurdles but they do have a small trampoline. Lord Vetinari bouncing up and down maintaining a perfectly deadpan expression...
Also, the rather offhand comment that maybe they should get some manacles, in case this happens again.
Carrot: I don't think we have a hurdle.
Vetinari: Well, I believe there's a rather large sporting goods store on Gleam Street. (Off Vimes' look) Just trying to be helpful, Commander.
Carrot: Technically, sir, traitors are to be dragged through the street on a hurdle. Then they're hung, drawn, and quartered. I know about hanging and quartering, sir, but I'm not quite sure how you're drawn.
Vetinari: Are you any good with a pencil, Captain?
Vimes: Are you taking this seriously?
Can you think of any reason why I should be carrying an inflatable donkey?
Well, you -
One that you wouldn't mind giving to your dear mother?
"I'LL CUT YER TONKER OFF'F YER YER GREASY - Oh, is that you, Sir Samuel?"
"Indeed, sir." The butler straightened up.
"Do excuse me one moment, sir KNOCK IT OFF YOU MOTHERLOVIN SONS OF BITCHES I had no apprehension of your presence, sir."
"Oh yes, sir. But as it transpired-"
"We knew there was somethin' wrong when the mutton barrels started to explode," muttered Private Bourke. "The biscuits was pretty lively, too. Turned out bloody Rust'd bought a lot of stuff even a rag'ead wouldn't eat-"
"And we eat anything," said 71-hour Ahmed solemnly.
"PRIVATE BOURKE YOU 'ORRIBLE MAN SPEAKIN' OF YORE COMMANDIN' OFFICER LIKE THAT YOU WILL BE ON A CHARGE I apologize, Sir, but we are feeling a little faint."
It's mentioned that Lord Rust suffers from Selective Obliviousness; if someone says something he doesn't like, he erases it from his mind. But when Unseen University's Dean reports that Leshp is gone, Rust finds himself unable to erase the Dean; There was too much of him.
Prince Cadram, in spite of being the Big Bad of the book, is something of an Upper-Class Wit who actually has sensible things to say about the way some people treat Klatchians, so he has some funny moments of his own. Including, after a large collision between his forces and Ankh-Morpork's, "Oh, dear. Perhaps I should have had them led by white officers." Seeing as the Morporkian army was, he timed that perfectly.