The easiest way is through a mother's death. The ones that come to mind are:
meta spoiler; multiple anime titles
that one episode of DanDaDan
that one episode of Violet Evergarden
first episode of Oshi no Ko
Others that I've found moving include:
Gundam: The Witch from Mercury
Umamusume season 2
Angel Beats
Belle
86
I guess a common theme is that these anime feature characters who persevered through hardships? Can't remember the plot of Angel Beats since it's been a while since I watched it.
Edit: Incidentally, WfM, Uma S2 and 86 are my top 3 anime.