Oh boy. Too much to mention. So many hard titles to pronounce to recommend. Currently reading rail gun. Currently watching kaichou wa maid-sama. Pretty good so far.
Recommendations:
Romance comedy - toradora, nisekoi
Action - akame ga kill, attack on Titans, is it wron to try and pick up girls in a dungeon?
Horror - another
Romance - clannad/after story
Slice of life - my teen romance comedy snafu
Sports - haikyu
Fantasy - no game no life
All I can think of off the top of my head.