A really good list, probably because I've watched most of it ;-) Among more recent titles, I really liked Planetes. Welcome to the N.H.K. is also very good.

Interspecies Reviewers. And I'm recommending it solely because it's been heavily censored recently, and I hate censorship.

I'd recommend:
1. Dragon Ball Z -sometimes shallow story, but great action scenes, with a powerful redemption story cropping up in seasons 8-9.
2. Mobile Suit Gundam 0079 (First Gundam.) - A bit slow in developing plotwise, but has great characters, and a beautiful art style.
3. Anything from Studio Ghibli. My Favorites are The Cat Returns, Nausicaa and Porko Rosso.
4. Rorouni Kenshin. Takes place in Meiji Era Japan. Like DBZ it has great fight scenes, but is, in my opinion, deeper insofar as the story goes.

There are so many.

Berserk: the first serie OR the 3 OVAs, the 2017 serie is shit, the manga is the best.
Trigun
Hellsing
Dorohedoro
Monster
Parasyte -the maxim-: there are also a couple of live action movies.
Noein
Serial Experiment Lain
Ghost in the shell
Texhnolyze
Gungrave
Dororo
Black jack


Mobile Suit Gundam.
Kyashan

These come on top of my head, I tried to list my personal favourites and stuff that wasn't listed previously.
Enjoy.

Its also legit funny, and amusing, I am enjoying the fuck outta of it.

Two series made by Nobuyuki Fukumoto:
- Kaiji - Ultimate Survivor & Kaiji - Against All Rules about a consummate gambler and his misadventures around gambling;
- Akagi about a boy who's unbeatable in mahjong (it may sound boring, but belive me, it's not).

Dragon Ball and One Piece are great, but I've always liked the manga better than the anime series; maybe because I read them first and didn't like the voices that much.

I don't watch a lot of anime, but Made in Abyss was nice enough,
and Erased is supposed to be good, too. I haven't watched the latter yet, I've only seen the live action adaptation so far.

Oh, and Aggretsuko is awesome, though maybe not what you're looking for? Then again, you said any genre. And you like Adventure Time, so you have taste. ;)

Berserk is a great place to start. If you're into dark fantasy.

Everything recommended with a few exceptions is so old... It really depends what kind of anime you're looking for. From the more recent ones I'd say:

Shounen:
Boku no Hero Academia - World where kids grow up with superhero powers, great characters/music
Hunter x Hunter 2011 (somewhat older but amazing)

Sports:
Haikyuu - best recent Sports anime by far imo, massive cast of great characters.

Alternate world:
Re Zero Kara Hajimeru Isekai Seikatsu - Starts off quite basic but gets dark fast and keeps getting better.
Tensei shitara Slime Datta Ken - Guy who reincarnates in an alternate world as a slime... comedy, obviously.
No Game No Life Comedy with some fanservice (and the movie NGNL Zero, which is vastly more serious than the series with the occasional fanservice throwback to the series but it's wonderfully made, worth watching even if you wouldn't like the main series)

I agree with one of the above that Ishuzoku reviewers (comedy) is pretty damn good but that borders on Hentai so if fanservice is not for you, this definitely won't be. It's basically a group of people in an alternate world reviewing alternate species brothels

Coming of Age-ish?
Sora yori mo Tooi Basho - Cute girls doing cute things (going to antarctica...) Part feel-good, part tear-jerker. 100% beautiful.
High Score Girl I + II - about two kids growing up in the age of beat-em-ups like street fighter.

Cardgame:
Chihayafuru - Every now and then there's this anime about a game that's either totally beyond me or I'd never play but manages to just be absolutely amazing in tension and passion/spirit (last kind of like sports series sometimes). This one's definitely great to watch.

Full Metal Alchemist: Brotherhood

That anime set the bar for me. No fillers. The story is always progressing. Quality animation. Awesome fights. Great characters. The best part is that it has a satisfying ending.

Kengan Ashura

Each episode has at least one fight. If you just want to see people beating the hell out of each other, then you need to watch it.

One Punch Man

An anime that somewhat pokes fun at superhero and anime tropes. It's funny and action packed. They managed to make it entertaining even if the hero can one shot almost any villain he comes across.

This.

Watched the first season a few months ago and it instantly became my favourite anime series. It's been ages since something has made me laugh this much - it's just utterly brilliant. And I'm not even that familiar with anime tropes and stuff.

Season 2 is not as good as the first one but still fun enough to watch. It showed how King is as overpowered as Saitama. The King Engine. Nuff said.

Depends on what genre you prefer in general. Action? Comedy? Sci-fi? Fantasy? Honestly, it's like asking - "What movies you recommend?" or "What books to read?".

I would agree with everything, exept the "satisfying ending" part. It was a huge letdown for me, especially antagonist's plan.

If yer old enough:

La Blue Girl
Bible Black
etc
========================================================= An otherwise good list, but most people that are worth their salt know that Naruto is for people who ride the short bus. ;)
============================================================ Great series What, no Howl's Moving Castle? :D

Also worth a mention: Little Nemo(film)...yeah, made for kids, but still fun imo.
===================================================

I dunno about others, but I can only stand so much of people shouting and punching each other before I would wanna punch my TV. o.0