ok so I'll start by listing my personal favorites and then I'll go into ones which are generally considered very good.
School Rumble
so School Rumble is a comedy. There's a romance background plot but that can mostly be ignored for the comedy. It also has some of the best characterizations IMO some of the characters are so fucking real and that's what makes the show work so well.
Saishuu Heiki Kanojo
so this show is about a girl that got turned into a military weapon and she accidentally falls in love. Mostly romance/drama-ish kind of a sad story definitely worth checking out.
Haikyuu!!
this show has some great characters as well. They use sport as a background in this show but you don't need to care about sport. This show has such great characters that it works even if you hate sport which I do

. if you know anything about MBTI just imagine an INTJ and an ESFP working together they make such a good team, it's like they took light-kun from Deathnote and Naruto from Naruto lol
Prison School
if you're a female then there is a high likelihood that you would enjoy Prison School, according to a
recent poll females are really enjoying the show. Probably cause the show has dozen of well written female characters. Gist of the Story is that a bunch of guys start attending a female only school. In the beginning they're trying to get out of this Prison and on the way they fall in love with multiple very well written female characters.
Yojouhan Shinwa Taikei
this show is about college life. pretty good show but kinda weird and confusing at times but definitely a great show.
Boku no Pico
so this show is greatly underrated and I admit that it's a bit slow in the beginning but once the action starts the show starts getting really good
definitely worth checking out.
these are just my personal favorites there some more general shows which are generally rated highly:
Durarara
The plot of this show is kinda hard to explain ... this show has many supernatural elements and it's also about gangs fighting it out.
Neon Genesis Evangelion
so this show is a must watch for every anime fan. This show at it's time tried to deconstruct some common Mecha anime tropes and cliches and
tries to criticize the whole Otaku culture which somehow backfired. Anyway a must-watch.
Death Note
so this show is about an INTJ who randomly finds a book which can kill anyone written in it. This INTJ then tries to reform the world by killing everyone who committed a crime. It's very funny and interesting if you like INTJs. Check out
Code Geass too if you like INTJs it's pretty similar.
Toradora
this is a rom com but a pretty good one. It's like School Rumble if School Rumble focused on romantic.
Shingeki no Kyojin
this is a good action anime but very slow paced not sure if you're into it. The gist of the story is that Titans are attacking humans for some reason and humans trying to form a defense to these titans.