Feel free to add any completely underrated shows to the list.
Just for the record: I've been an anime fan for more than half my lifetime and the below anime are my favorites in descending order:

1. No. 6
2. Puella Magi Madoka Magica
3. Natsume Yuujinchou
4. Magi Series (Labyrinth of Magic, Kingdom of Magic, Sinbad no Bouken)

The first two have yaoi + yuri themes, so I kind of understand why they maybe wouldn't have made it so big in mainstream anime media (BUT THEN YURI ON ICE??? REALLY??? WHY DOES EVERYONE ALWAYS TALK ABOUT IT?? NO OFFENSE, IT'S NOT HORRIBLE BUT DOES IT REALLY MERIT SO MUCH ATTENTION? Otabek x Yurio for life tho).

I seriously don't understand how such stellar shows can sometimes seem to go completely unnoticed; ESPECIALLY NO. 6!!! I'll see references for PMMM and Natsume Yuujinchou, and rarely for the Magi series-- BUT NEVER NO. 6!! The narrative is told beautifully, the world is well developed, and the characters are so full and brimming with life. The main characters' relationship isn't the only focus (Because there's actually plot... Not YOI, haha) and it's realistically gradual and so romantic, and not forced at all. You get to know the characters before they're forced into a relationship, which I really feel is not common in many stories!!! I LEGITIMATELY NEED SOME EXPLANATION AS TO WHY I'D NEVER HEARD OF THIS ANIME BEFORE!!! WHY DIDN'T IT MAKE IT BIG???

NO. 6 IS AT LEAST 40% OF WHY I'M LEARNING JAPANESE!! (That's a huge percentage, since I know hundreds of shows, mangas, doujinshis, and mangakas) I really need to read the source material, the novels...

But why? Why SAO? (It... Quickly went to crap) Why YOI? (Just... So overrated. The characters feel horribly 2D but somehow OtaYuri struck a chord with me) Why not the anime that explore life and reality so beautifully? (My first and third fav anime in particular) Why not the anime with such raw, powerful beauty? (PMMM FTW)

Again, feel free to add on other underrated anime... I'd love to hear some... I'd also like to hear why certain anime or such high quality never cause so much of a stir? Seriously, go on a rant if you want, haha...