I'm a huge anime fan, it's I guess my main hobby. So, here are some different genres for animes for you and it doesn't matter if you either never watched anime before or just need a new one to start. Side note: I'm not a fan of Slice of Life so this genre won't be shown here.

Fairy Tail

anime, charles, and happy image Image by Nashi<3
Fantasy | Action

It's a typical long term anime, with around 7 seasons right now and each have around 40 episodes. If you need something different then One Piece, Naruto or Dragonball you should try this one. It's about the magic guild Fairy Tail that fight against illegal guilds or do missions.

Tokyo Ghoul

tokyo ghoul, kaneki, and anime image badass, mask, and kaneki ken image
Fantasy | Horror | Action | Splatter | Drama

This is about a world where humans and ghouls life together but ghouls aren't able to eat anything else then humans and so there are searched and killed. The tension keeps up and I think it shows good how a life changing situation can change a person.

Mahou Tsukai No Yome

anime image the ancient magus bride image anime, my posts, and mahou tsukai no yome image mahou tsukai no yome, elias ainsworth, and hatori chise image
Fantasy | Drama | Romantic

Aka The Ancient Magus' Bride is a fantasy anime with romantic next to it. It's about Chise who learns magic and she have to face all the problems of the world of magic. It's pretty new, so at the moment it only have one season.

Shingeki no Kyojin

titan, attack on titan, and micasa image Abusive image
Action | Horror | Fantasy

Aka Attack On Titan.This anime is filled with impulsive moments. For everyone who loves action this is perfect it's about the titans. There are only few humans left who tries to survive in a world of titans who only eat human beings.

No Game No Life

shiro, anime, and no game no life image anime, shiro, and sora image
Comedy | Fantasy | Adventure

It's about two siblings and they call themselves Blank, they are gamers and because of this they get the admission to the world of games. It's fun to watch and there are a lot of funny scenes but also a lot of action filled scenes.