I really liked Uzumaki and Death Note. Both are sort of horror though, not sure if that's your thing or not.
Some of my favorites are fullmetal alchemist, noragami, and soul eater and I second death note. I also liked d.gray man and black butler. I'm blanking on other ones, but I'm sure I could think of more. Hope that helps
Fullmetal Alchemist, Neon Genesis Evangelion, Berserk.... I've read so many I just can't think of them right now.
If you're looking for something LGBT (and more specifically Trans) Friendly, go with Wandering Son. Link: http://kissmanga.com/Manga/Hourou-Musuko There's also Tokyo Ghoul and by extent Tokyo Ghoul:re which includes 3 Trans characters, but only one of them isn't a stereotype/joke character and he doesn't appear until Tokyo Ghoul:re. Link: http://kissmanga.com/Manga/Toukyou-Kushu
As you can probably tell from the replies, Fullmetal Alchemist is a pretty vital manga to read! I'm also a fan of Kekkaishi(Action), Death Note(Thriller) and Nichijou(Comedy)
Death Note is awesome (although it's more Crime/Thriller than Horror). If you want: Romance - Mars (tw: rape, suicide, and violence; otherwise a great 'Beauty and the Beast' story about an artist and a motorcycle racer with a deathwish) Fantasy - Yu Yu Hakusho (great fighting manga with demons and alternate dimensions and stuff) Slice of Life - Horimiya (another romance but it's literally just two teenagers that start dating, they make curry, watch horror movies, and talk to their friends) Crime - FAKE (Boy Love! tw: lots of blood, death, murder, drugs; decetives falling in love and kicking ass!) Sci-fi - Gundam Seed (gundam is fairly self-explanatory...right?) Sports - Chihayafuru (technically a girl's comic, about competitive karuta, lots of Japanese cultural things, very interesting) Also fairly popular right now: Sword Art Online (life in a vr game), One Piece (pirates!), Kagerou Project (singing), K [Project K, Kings] (superpower gangs), Haikyuu (volleyball), Kuroke no baseke/The Basketball Which Kuroke Plays (basketball), Noragami (gods),...