Dragon King of Arms announces all his plans to the hero in the first chapter through puns. If any of the Watch had had that kind of sense of humour, the book would have been about fifty pages long.
Vimes basically swears Dorfl in as a police officer (and thus helps to redefine the existing power structure between humans and golems) because the establishment dared him to.
Better, he swears in Dorfl, and several zombies because they told him that there were too many dwarves and trolls.
Some of the 'Golems-aren't-alive' believers try to convince Vimes that it wouldn't be murder to kill one, and so the Watch can't stop them. Vimes threatens to arrest them for damage to private property instead, since all Golems were at this point 'owned' by their masters.
Dorfl getting the priests to deflect their anger from Vimes to each other, while agreeing to debate them on his (non-existent) day off.
'EITHER ALL DAYS ARE SACRED, OR NONE ARE. I HAVE NOT DECIDED YET.'
An atheist who's immune to lightning bolts...
Angua knows Cheery is wearing silver chainmail, and may hate her once she finds out she's a werewolf, yet doesn't hesitate to grab the chainmail in her mouth (burning herself badly) to rescue her dwarf friend.
And she didn't have to bite the silver. She could take an arm or leg but that would hurt Cheery, so she goes for the chainmail which will only hurt her.
Doubling as a Crowning Moment of Humanism, Philosophy, Morality and just about anything worthwhile, the moment when Dorfl realises he owns himself and is responsible for his actions. Not only is it marked by the pronoun change - from 'it' to 'he' referring to the golem - but there also is this, incredibly powerful sentence:
Not Thou Shalt Not. Say I Will Not.
Vimes' first scene, dealing with an assassin in the utterly casual way that can only be the result of long practice.
Angua letting herself be taken hostage by three unlicensed thieves, so she can teach them a lesson.
An off-screen one. After the main events of the book Vimes called the conspirators who caused all this to the palace. It isn't explicitly said what kind of conversation took place but it certainly ended with an axe being buried in a table and the conspirators leaving with strong memories of Vimes' ancestor cutting off the head of a king. Since it's in a room usually reserved for important meetings Vetinari decides to leave it there as a conversation piece.
Vetinari figuring out exactly how he's being poisoned but letting it continue to a small extent so that Vimes will have to try to solve the crime in a very Vimes-like way, which is what Vetinari wants him to do.
Drumknott: I think if Vimes did not exist you would have had to invent him.