Some personal favorites:

Classics:
✦ [Puella Magi Madoka Magica]( https://myanimelist.net/anime/9756/Mahou_Shoujo_Madoka%E2%98%85Magica )
✦ [Your Lie in April]( https://myanimelist.net/anime/23273/Shigatsu_wa_Kimi_no_Uso )

Psychological:
✦ [Happy Sugar Life](https://myanimelist.net/anime/37517/Happy_Sugar_Life )

Slice of Life:
✦ [Chihayafuru](https://myanimelist.net/anime/10800/Chihayafuru)
✦ [Fruits Basket](https://myanimelist.net/anime/38680/Fruits_Basket_1st_Season)

Moe Slice of Life:
✦ [Comic Girls](https://myanimelist.net/anime/35756/Comic_Girls)
✦ [Quintessential Quintuplets](https://myanimelist.net/anime/38101/5-toubun_no_Hanayome)

Seinen/Shounen:
✦ [Bungo Stray Dogs](https://myanimelist.net/anime/31478/Bungou_Stray_Dogs)

Romance:
✦ [Rascal Does Not Dream of Bunny Girl Senpai]( https://myanimelist.net/anime/37450/Seishun_Buta_Yarou_wa_Bunny_Girl_Senpai_no_Yume_wo_Minai )

Monogatari:
✦ [Bakemonogatari (and subsequent seasons)]( https://myanimelist.net/anime/5081/Bakemonogatari )