Sorry, been writing a preview that has to go up tomorrow morning.
In no particular order:
Currently, I'm digging Log Horizon, Aldnoah Zero, Psycho Pass, Ping Pong the Animation, Monthly Girls' Nozaki-kun, My Teen Romantic Comedy SNAFU, Kuroko's Basketball, and Jojo's Bizarre Adventure.
I read the Shonen Jump Three: One Piece, Naruto, and Bleach, but I don't watch the anime because my time is limited.
I'm sure there's more, but that's off the top of my head. I'll do mostly anything if it's got a great story, but I definitely have a fanservice threshold at this point. I dipped out of fan-favorite Sword Art Online because it had an interesting premise, but they dropped in favor of harem show tropes and fanservice. (Log Horizon delivered more on the same idea.) Things like High School DxD and High School of the Dead tend to get ignored; you have to really up your story gamto get me past that kind of excessive fanservice.