Probably can't call it underrated, but some of Hayao Miyazaki's lesser known work is also some of my favorite.

One example is the On Your Mark [1] music video, which is possibly the only time he went into cyberpunk, and despite being a few minutes long and having no dialog it has amazing world-building and storytelling.

Future Boy Conan (Mirai Shōnen Konan) [2] is a great TV series by him that doesn't get mentioned enough IMO.

1: https://vimeo.com/394801904

2: https://en.wikipedia.org/wiki/Future_Boy_Conan

Serial Experiments Lain - I'm still waiting on IPv7.

There's been a few recommendations already for Serial Experiments Lain, but whilst I did enjoy it, for my money Texhnolyze by the same creator is absolutely incredible (and much less discussed). It's very slow going though, particularly at the start, but I still think about the last several episodes on an alarmingly regular basis (having watched it years ago).

I also recommend Now and Then, Here and There: a fish-out-of-water fantasy show in which the main character acts like a stereotypical comedy protagonist but the world he gets transported to is an absolute wasteland ravaged by war and environmental degradation. Unsurprisingly also not a light-hearted watch.

If Hayao Miyazaki can be considered the Steven Spielberg of anime films, then I personally consider Satoshi Kon as the Stanley Kubrick. My top 3 from his filmography are “Perfect Blue”, “Tokyo Godfathers”, and, of course, “Paprika.”

Haven't watched much of anime, and haven't watched any for more than a decade. But back then I had huge impression from Azumanga Daioh. Nothing special in plot, just a year in the life of a few schoolgirls. But such lively and unique personages, I remember I had lump in the throat when I watched the last episode, as if I was saying farewell to close friends that I will not ever see again.

If we're going for obscure, I'm going to recommend Armitage 3, which is a Ghost in the Shell-esque cyberpunk action adventure. Same energy, and definitely better than a simple clone.

Also a mention to Wolf's Rain. It's a post apocalyptic dystopia where wolves can pretend to have human form, and try to survive. It sounds bonkers but it's charming and it works.

I really like historical settings:

House of Five Leaves: A robinhood criminal gang

Angolmois - Genkou Kassenki: Mongol invasion of Tsushima in 1248

Onihei: Crime fighting in the Meiji era

Onmyouji: Heian era magic

Shouwa Genroku Rakugo Shinjuu: Rakugo performers in the Shouwa

Glasslip: Not historic, a modern day in the life story

Maiko-san Chi no Makanai-san: also modern, a Kyoto story of geisha apprentices

Heike Monogatari: A great telling of a Heian era power struggle

There are so many more...

Welcome to the NHK - A black comedy about hikikomori, the anime industry, cult religions, conspiracy theories, pyramid schemes, suicide, and other topics. Not cheerful topics, but it is funny and has a lot to say.