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Tear Jerker: Jingo
Vimes is leveling a crossbow at a warmongering prince just as he realizes (as the prince knows) that he can't just arrest a ruler, even if he says he can. At the end of his rope, he then hears a malfunctioning day planner start telling him what would have happened if he hadn't pursued the prince: namely, he would've stayed to fight the war in Ankh-Morpork, where he and all the other watchmen would've died. The planner starts rattling off the names and times of each casualty...
Even though you know most of those names are standing right there, completely not dead, it's still heartbreaking.
...and a fair bit of Fridge Horror when one considers the alternate Vimes, whose Disorganizer likely went on with cheery little reminders of "Pleasant dinner with D'reg wiseman," "Discover truth behind assassination plot," and "Charge into tent, arrest military commanders, arrest both armies before they start fighting, hold off war long enough for Vetinari to do his thing"... exactly as he and everyone in his Watch is dead or dying, and Angua is stuck in the Klatchian desert without a way home or any idea that this is happening. The novel itself specifically mentions that both Vimes would get to know what would have happened...
It's even sad to hear the progression of the Disorganizer's imp. It's initially sort of pitiful, never being able to keep Vimes' appointments straight, but when it starts reading them out before they happen, he seems almost...proud. Then when they stop matching up, he starts off confused, and gets worse and worse until his words make it sound like he's a malfunctioning computer program. The imp is torn between the world as he knows it should be and the world how it is, and it...broke him.
For extra horror, listen to that part in the (unabridged) audiobook version.
It's hard not to feel for Leonard when he sets the Boat adrift in the sea after learning what other people would use it for.
The deaths of Privates Hobbeley and Webb, killed by 71-Hour Ahmed after he and Vimes were mistakenly attacked by Ankh-Morpork soldiers. The others don't seem to blame Ahmed - who was, after all, just defending himself - but as Vimes said, "But...one moment they're alive-"
"I tell you this, girls: I wish I'd settled for the ten-dollar version. Don't you just sometimes wanna sit down and cry?" Nobby taking to being a woman (leading to more crossdressing in later books) is funny, but behind the laughs it's hard not to feel sorry for him: The ugly, temperamental and female "Beti" might get degradatory comments about her looks, but overall she's still treated better by men and women alike than plain old Nobby Nobbs.
"All in all, she considered, she was jolly lucky."