Black Cat - I don't remember if I actually watched the anime, but I read the manga, and I remember it being pretty good.
Darker than Black - Chinese Electric Batman.
FMA/FMA:B - They're both good, but Brotherhood is better, imo.
Kokoro Connect - This probably falls under the category of 'weird shit with teenage kids', but it's such a good anime that I had to put it on here.
One Punch Man - Just watch it. It's so good.
Samurai Champloo - Great anime. Amazing soundtrack.
Steins;Gate - Watch at least twice.
Tengen Toppa Gurren Lagann - Widely regarded by me as the greatest mecha anime ever made.
NHK ni Youkoso! - Depression.
I'll list some more that I'm not sure if you'll like but I enjoyed.
Chuunibyou demo Koi ga Shitai!
Kono Subarashii Sekai ni Shukufuku wo!
Little Witch Academia: Mahoujikake no Parade
Monogatri Series - I'm not going to link them all. That would be a pain. Here is a link to the order you should watch them.
Panty & Stocking with Garterbelt