This is a good topic to step out of the mainstream a bit and discover interesting and/or unusual stories
I don't watch anime very much, so my list is composed of manga:


Onani Master Kurosawa: My all time favorite, deals with the theme of isolation, which is a theme that always mess with my feelings. If you decide to read it, do not turn away because of the plot, in the end you will see it was worth it


Legend of Koizumi: World leaders playing mahjong as a way of making diplomacy. The only place you can find things like Vladmir Putin, Adolf Hitler and Pope Benedict XVI playing mahjong together.


Vinland Saga: Puts manga and Vikings into one thing! There's no way you wouldn't enjoy that! But it is not only the vikings that make it good, it has the best character development I ever found in manga.


Welcome to N.H.K: Yet another one that deals with isolation.


Hotel: A 40 page one-shot. Impossible to read it all without crying for the little robot.


What about you? What are the stories you love but no one heard about them?

I love the Limit series by Keiko Suenobu, I haven't finished it buts it's great. It's like a modorn day Lord of the Flies with 5 Japanese school girls from different cliques who survive a bus crash that kills all their classmates, teacher and driver. Then they must then learn to live and survive together while fighting human nature and hoping to be saved. A great series. It's a shame most people don't know of it, especially since Ms. Suenobu wrote the more known series Life. But then again I think just by it being underground it's even more special in that right.