I just finished watching a really good one from netflix called "Your Lie In April" its so damn good and it almost made me cry. Normally I don't watch anime but it was 5 solid stars and it deserves that, it's a visual masterpiece too.
Edit: i still can't believe one punch man hasn't been mentioned .
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Edited by meh: 6/27/2016 10:57:24 PMWord of advice, look at the tags. If you see the ecchi or harem tag, you want to avoid it. My recommendation would be 'the future diaries', which sort of dabbles in most genres, including action, adventure, tragedy, comedy (made me laugh anyway), mystery, physchological, sci-fy, romance, fantasy(sort of, vaguely. I'm basing this off the god). Best character development I have ever seen, in regards to both backstory and the changes to the characters in the show. Mc starts off as unbearable, becomes great through loads of small changes. Story's good, got interesting twists. If you do watch it, don't watch the OVA. Most people like it, but i liked how it originally ended.