Probably missing or already misplaced many things. Will add and take away as I go. Some of these I consider "bad" or "meh" but include nonetheless.

Fantasy

Claymore
Berserk
Fate
Magi

Action/Adventure

JoJo's Bizarre Adventure
Fullmetal Alchemist: Brotherhood
Samurai Champloo
Afro Samurai
Trigun

Drama

Welcome to the NHK
Tokyo Magnitude 8.0
Kokoro Connect
Spice and Wolf
Baccano

CGDCT

Non Non Biyori
YuruYuri
Lucky Star

Mecha

Code Geass
Gurren Lagann
Eureka Seven
Evangelion

Romance

Toradora
Clannad (mostly for Afterstory, but something you should watch at some point)

SciFi/futuristic/Space

Legend of the Galactic Heroes
Mardock Scramble
Steins;Gate
Knights of Sidonia

Thrillers/Mystery/Psychological

Monster
Kara no Kyoukai
Terror in Resonance
Death Note (loved it until a certain point like most others)
Durarara

Comedy/Parody

School Rumble
Panty and Stocking
Ninja Slayer
Prison School (ecchi)
Nichijou