This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / American Gods
Some of the interludes are really depressing:
The story of Hinzelmann, the child in the dark
The story of Wututu and Agasu
It's sobering that Laura died because she cheated on Shadow with his best friend, and was asking for a handjob while she was drunk and he was the designated driver. It's even worse when Laura starts to look out for Shadow, while resenting that he brought her back by accident.
When Shadow and Laura are finally reunited, Shadow after coming back from the dead and Laura ... well, as well, note somewhat. It's not really clarified if it was permanent. But she'd stabbed what became the spear of Odin through her stomach to get to Mr. World. and Shadow asks her if he can bring her back. She tells him she'd rather go the other way. He does so, with a coin trick.
Shadow finding Allison's body. He can see the fear in her wide open eyes and the tears still frozen to her cheeks.
The realization that hits Shadow and the reader: that Mr. Wednesday was his father and used him as a sacrifice to start the war between the old and new gods. Shadow doesn't even have good catharsis because when he meets the original avatar of Odin in Iceland, that Odin isn't the conniving Mr. Wednesday.
Also the fact that Shadow is an avatar of Baldur, and that not every myth of his death involve a sacrifice. Some myths have Loki getting Baldur killed by mistletoe deliberately, and Odin going Papa Wolf by asking for Hel to deliver his son back to the living realm. Mr. Wednesday and Low-Key Lyesmith could have chosen a different two-man con . . .
Monarch of the Glen
Shadow's Heroic B.S.O.D. following the novel, where he's Walking the Earth and doing his thing. He doesn't even raise an eyebrow when Smith and Alice offer him a job as a bouncer for the weekend.
How Jennie describes monsters to Shadow: you know you've met a monster when you're dinner. She is a troll from the old days, and Baldur is a Norse god considered a monster by Smith and Alice.
Grendel's mother starts wiping the blood off her son's face after Shadow beats him and then returns Grendel to her. She says with grim satisfaction that at least this time her son is alive.
To thank Shadow for not killing her son, Grendel's mother tells Smith and Alice that if any harm comes to Shadow, she threatens to hurt them. This is sad because Shadow still had to fight Grendel, though he didn't want to be a monster.
How Moira and Ollie met: they cheated on their partners at the time.
Moira and Ollie's reactions when Shadow tells them that Cassie asked him to say hi to them. Moira then reveals that Cassie was her girlfriend, while Ollie is disturbed enough to check that Cassie's where he buried her alive.
The Reveal that Cassie was Dead All Along and she wanted Shadow to avenge her because he was the only one who could see her. Also that Ollie murdered her even though he had already won over Moira.
Cassie's apology to Shadow for using him to avenge her and says that he must hate her. He tells her that he doesn't as she fades to the afterlife, and says he wish he could have met her while she was alive.