Alright, lets start with the horror gender : My personal favorite is Elfen Lied. I actually have a tatoo from this one. It's not the greatest, but it's without any doubt the one I enjoyed most.

Hellsing ultimate : If you like action, gore and OP characters, well this is as good as it gets. Satisfying to watch.

Higurashi (When they cry): Cute and charming characters... then it quickly turns to horror. It's very deep, it takes a long time to understand what's happening, but you will get mind blown hard.

Romance : the gender is garbage imo, but Toradora and Chuunibyou are great.

Comedy / humor : Shinometa : Humor about NSFW

Kono Suba : Overall great show

Psychological : Shinsekai Yori : Humanity as evolved to a race of psychic being that lives in harmony. Humans cannot harm each other. But all great things have some dark secrets.

The monogatari series : Greatest animations of all time, excellent cast of characters. It's basicly many short stories about the unatural. You can watch it simply for it's humor, but if you look deep into it, you will ponder a lot about a wide variety of subjet.

All categories : Steins gate. A simple 10/10 show about time travel. There is everything, action, a bit of horror, romance, comedy, character devellopement.

Alright, I'd like to write even more, but this should be way more then enough. These are all 9/10 or 10/10 in my opinion. If you don't really know what you are looking for, go with steins gate. Haven't heard anyone complain about this one.