This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Shinryaku! Ika Musume
Shinryaku! Ika Musume is a light-hearted comedy with seven-minute stories. Then there's the last story in episode 5, "Won't You Keep It?". You know it's going to end on a sad note, but the twist — such a simple twist — makes it so much sadder. (It's only seven minutes long, and it ends with the last few seconds of a Mood Whiplash, yet this troper cried for much more than seven minutes afterwards.)
Ika discovers what an umbrella is, and she eventually comes to use it as a weapon. Then it gets run over by a car. During the end credits for this episode, Ika holds the innocent, brave, crippled remains of the umbrella by the handle.
Ika and friends head to the amusement park that Eiko's family used to spend happy days at when they were little.... to find that the economic downturn chipped it into a single teacup ride in the middle of a small city block, with a single elderly employee handling all the duties of the park. ... and they just happen to head there on the park's final day before it officially closes! Eiko promises the employee that they shall spend the whole day there to send it off with pride! This sequence will be very emotional to those in similar situations. And then there's the Happy Flashback Eiko has of her parents, which causes her to start crying.
Season 2. Mini Ika gets lost in the backyard of her owner's home, and goes on an adventure much like Honey, I Shrunk the Kids. Although she braves the dangers, she has no idea she's even that close to the house, and she keeps getting flashbacks on how happy she was with Eiko, and is convinced she'll never see her again. And she starts crying. In the rain...
In episode 12 of Season 1, after Ika cuts her tentacle hair after they stopped working and started to talk normally, Takeru finally loses it and chucks a float toy at Squid Girl, then he breaks down sobbing and proclaiming that he wanted the old Squid Girl back.