The whole sequence where Kvothe loses his parents and his extended family.
And the following scene in the framing story, when Kvothe goes out to the woods and cries over the awful memory.
Kvothe's cruel stay in Tarbean
Particularly his father's lute being broken on the first day.
And Trapis, who's basically a heartbreaking moment on two legs. Think about it: He spends every minute, every day, every year on his bare feet in a cold stone cellar taking care of hundreds of homeless children - lonely, starving, defenseless, broken, hated children - giving them everything he has, which is so little it cannot be measured. Nothing he does can ever make a noticeable difference in the larger picture of the city, and the most he can ever hope for is to see the back of maybe one kid in a hundred who makes it out. Kind of makes you think there's good people in the world.
And taking a life-threatening beating,then almost dying alone in the snow on the equivalent of Christmas. And the only person to stop and help him is dressed as the worst of demons, and supposed to be out causing the worst of mischief, and he does it while a woman tries to drag him away to have fun.
To have fun and to not to be framed for the beating.
Kvothe crying about missing his mother in Auri's arms while he's under the influence of the plum bob.
Kvothe's argument with Denna after he first heard the Song of Seven Sorrows. Breaks this troper's heart every time. So true.
The whole sequence after Kvothe kills the fake troupers is god awful. We get to see that one of the girls who has been raped four times a night repeatedly has caused her to be driven the next best thing to catatonic. Not to mention Kvothe's own reaction to them killing and impersonating a troupe is heartbreaking, you can just feel the sadness underneath the anger:
Kvothe: "You thought you could fool me?" I said, feeling my anger coiling inside me like a spring. "This is my family! How could I not know?"
After Kvothe follows Denna without her knowledge, he learns some interesting things about her. He describes it by mentioning the philosopher Teccam, who had this to say:
Kvothe: Secrets of the heart are different. They are private and painful, and we want nothing more than to hide them away from the world. They do not swell and press against the mouth. They live in the heart, and the longer they are kept, the heavier they become.
Teccam claims it is better to have a mouthful of poison than a secret of the heart. Any fool will spit out poison, he says, but we hoard these painful treasures. We swallow hard against them every day, forcing them deep inside us. There they sit, growing heavier, festering. Given enough time, they cannot help but crush the heart that holds them.
Modern philosophers scorn Teccam, but they are vultures picking at the bones of a giant. Quibble all you like, Teccam understood the shape of the world.