New anime worth watching: I don't know the ching chong titles for some of these btw-
Akame ga kill! - people have weapons that give them powers, they fight the corrupted capital, blah blah people f*cking die and feels.
Terror in Resonance - two kids terrorize tokyo in the most passive-aggresive manner possible then they turn out to not really be terrorists which is kind of stupid but it might be building up to something.
Alnoah Zero- astronauts get sent to mars and form their own empire based on ancient technology they find allowing them to control super mechas. they attack earth and kill lots of people but the protagonist is all "not on my watch you mars c*nts" and fights them with a training mecha which is a huge spit in the face. Pretty reasonable characters despite this one chick who lost her dad, i mean get over it. Tokyo Ghoul,
All are ongoing and relatively good.
For finished anime, who cares there's a million lists out there it's all based on preference.
Cowboy bebop/samurai champloo are starters i recommend to everyone because if you dislike them you should highly consider sudoku.