This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Feet of Clay
WORDS IN THE HEART CANNOT BE TAKEN. Then, of course, this being Pratchett, he breaks out some hilarious Mood Whiplash. This tends to reduce readers to a squeeing, bawling, hiccuping-with-laughter mess.
The deaths of William and Mrs. Easy, along with the description of how the poor live in Ankh-Morpork and Vimes' memories of his youth in the ghetto. Mrs. Easy's death is particularly hard to bear: when William fell ill, she stayed up all night among the poisonous candles looking after him.
Worse still is that Vimes is literally the only person outside their immediate social circle who knows and cares they've died so unjustly. Even Carrot — who's supposed to know and love everyone in Ankh-Morpork — did not know her.
Vimes: Then it's something we're not seeing, damn it! People are dead, Captain! Mrs. Easy's dead!
Carrot: Who, sir?
Vimes: You've never heard of her?
Carrot: Can't say that I have, sir. What did she use to do?
Vimes: Do? Nothing, I suppose. She just brought up nine kids in a couple of rooms you couldn't stretch out in and she sewed shirts for a tuppence an hour, every hour the bloody gods sent, and all she did was work and keep to herself and she is dead, Captain. And so's her grandson. Aged fourteen months. Because her granddaughter took them some grub from the palace! A bit of a treat for them! And d'you know what? Mildred thought I was going to arrest her for theft! At the damn funeral, for gods' sake! It's murder now. Not assassination, not politics, it's murder.
The situation of the golems. You have these quiet creatures who would never harm anyone being categorized as non-sentient, enslaved and despised, working in extreme conditions, walled-up, put in deep pits etc. and they are left there for centuries, lost and forgotten and unable to scream or voice any emotion. It would count as And I Must Scream except that they can commit suicide... most of the time.
Carrot: ...But what do you [golems] actually want? Dorfl(writing on a slate):RESPITE.
The golems were so desperate for freedom that they tried to make their own leader. They wanted him to be so perfect that they filled him with so many rules that he went mad. Their guilt and remorse over what they had done. CLAY OF OUR CLAY.
When Dorfl is given the gift of his own ownership.
That last parting smile from the King golem. No matter how badly screwed-up he'd turned out to be, he knew the golems had found a savior from bondage in Dorfl after all, and was glad.
More with their savior. He decided he would free his fellow golems...by working hard, for days on end until he could afford to buy one and give it to itself. Then they would work hard, for days on end until they could afford one more. They would, without ruining anyone's day, breaking any laws or spilling a single drop of blood, become free... by their own hand.
The image of the golems trying desperately to bring someone back to life by copying their own chem and slipping it in the dying man's mouth. Even worse, the person who has to explain it to them is the dying man himself.
''We don't work like that...we make our own..."
The words, "I have given it some thought, and I have come up with the following response - arseholes to the lot of them, sir" shouldn't be Tear Jerkers, but they are.
When the golems start committing suicide:
Dibbuk had never been very wordy. He'd carry red-hot iron, hammer sword-blanks with his fists, clean out clinkers from a smelter still too hot for a man to touch... and never say a word. Of course, he couldn't say any words, but Dibbuk had always given the impression that there were none he'd particularly wanted to say in any case. He just worked. These were the most words he'd ever written at any one time. They spoke to Stronginthearm of black distress, and a mind that would have been screaming if it could only have uttered a sound.
THE OLD MEN HELPED US! THOU SHALT NOT KILL! CLAY OF MY CLAY. SHAME. SORROW.
What makes this worse is that you realize that the golems are inherently gentle creatures who are so ashamed and saddened by the acts of one of their own that they are literally Driven to Suicide... and then the humans persecute and beat them to death because of their fear, the golems not even able or willing to fight back!
And if they'd just waited a few more days, the freed Dorfl may have been able to convince them to live on, eventually to work alongside him in earning their fellows' freedom. But a golem with a task to carry out doesn't dawdle about it, even if that task is methodically sawing its own head off.
The King Golem in general. If a golem can be considered a robot, and its brain a computer, what happens when you give it so many directives that it would be impossible to follow all of them? And just about all of them are absurdly vague. And this is not something that can pick and choose which directives it can follow: it was supposed to follow all of them, no matter how impossible or ill-defined they were. No wonder it went insane. Even if it was a multiple murderer, it's still one of the biggest victims in this story.
This whole issue of "too many directives, not enough of them made specific" could be seen as a Shout-Out to RoboCop 2. Murphy also goes insane because of this, and fixes the problem with a bit of self-administered high voltage therapy.
In many ways, Nobby's sub-plot. His attempts at fitting in with the upper class are funny, but have a pretty heart-wrenching subtext: He genuinely thinks he's making friends and getting the respect he's never had in his life, but he's just being used and in reality his "friends" can barely repress their disdain for him.
Poor Mildred Easy will be burdened for the rest of her life by the knowledge that something she brought home from the palace killed both her baby brother and her hard-working old grandmother. And she and they had done absolutely nothing to deserve such a fate.