Oh boy my list is expansive. These are some of my favourites though
Owari no Seraph (Apocalyptic world, includes vampires)
Aoharu x Kikanjuu (It's about these things called survival games, exciting and light-hearted, only one season though)
Haikyuu!! (Volleyball. It's intense)
Kuroko no Basuke (Another sports anime; Basketball. Like Haikyuu but like 3x more intense)
A Boring world where the concept of dirty jokes doesn't exist (Fricken HILARIOUS. Totally not PC though. You have been warned)
Hamatora (An underrated show in my opinion. They got rad super powers)
Attack on Titan (I'm sure you've heard of this one)
K-Project (more rad superpowers)
Karneval (Another light-hearted show, a little hard to follow sometimes though)
Noragami (God's n stuff. It gets heavy)
Baccano (Just incredible. Mafia and what not. However it follows a whole bunch of little stories part of bigger plan, can be hard to follow)
ERASED (A very recent INCREDIBLE show. Time travel and drama, ooo)
The pet girl of Sakurasou (This is a feels trip. Romantic Comedy)
Kaichou wa maid-sama (Another romantic comedy)
Nagi no Asukara (It's cute. And feelsy. Really cool concept though)
Tokyo Ghoul (This shit will fuck you up. I still cry even now)