I'd have to say that my absolute favourite genre is drama. I consider myself to be a very emotional person and I love anime that has depth and meaning. Violet Evergarden is my current favorite, while it's rather slow paced, every single episode has such purpose, and has never failed to make me weep. Violet's character development is tremendous and to witness her growth as an individual is absolutely heartwarming. The underlying message of love, mourning, and emotional recovery throughout the story is so powerful. Your Lie in April is another favourite in this particular genre.
Fantasy anime is another genre I enjoy, InyuYasha, in particular.
Post-Apocalyptic anime is another genre I surprisingly like, as Attack On Titan is one of my all-time favourites.
Here's a list of other anime that I love (that I'm not quite sure what genre they fit into): Children of the Whales, Vampire Knight, Red Data Girl, etc.