Sooooo, I started writing this before I saw:
So here's a list of non-sci-fi anime, (but Steins;Gate isn't hard sci-fi though), but all the animes on this list are very good, and are definitely worth watching:
I have watched about 40-50 animes so far, here are some of the best I've watched:
Hellsing Ultimate, the first anime I watched at the time I got into anime, it has also been the source for the past 4 (not my current) avatars,
Noragami,
Drifters, this is based on a manga by the same guy (Kouta Hirano) who made the Hellsing manga, I've only watched the first 2 episodes, and it hasn't finished airing, but it's a great anime so far,
Overlord,
Highschool DxD, my all time favorite anime, for reasons you will see if you watch it, (Note, only watch this if you either use headphones or live alone, and make sure you screen is visible to only you, )
Kill la Kill, I've only watched about half of it, but it's a good anime,
Rokka no Yuusha,
Soul Eater,
Mirai Nikki (AKA Future Diary),
Steins;Gate,
One Punch Man,
Assassination Classroom,
No Game No Life,