Of course I won't like everything from those genres, but still, I like these.
Also, I like:
-Psychologic stuff, when it goes into your mind and you have to think to understand the stuff and etc. It's generally really deep.
-Sad stuff, and I mean really sad or depressing, rather than boring drama.
-Stuff you can relate to, like Yotsuba&!, Crayon Shin-chan, Chibi Maruko-chan and Azumanga Daioh, which are pretty realistic when it comes to life, but still pretty happy.
-When it can change you and how you think, generally for the best, or it can teach you something about life, like Usagi Drop.
Oh man, and it can count as stuff you can relate to, but on a less common way.
-Dark fantasy, I generally enjoy this too, along with some horror-like stuff. Especially when it crosses with some of the above too.
-Parody-like stuff, that's pretty self-explanatory, things like DD Hokuto no Ken and Dr.Slump.
-Serious and (considerably) realistic things, like Crying Freeman, Hokuto no Ken, Vagabond (which is something I liked, but I'm always lazy to read manga when it gets too long, not to count, being too long makes it get expensive and all of that).
Shounen and Seinen both work for me. I enjoy Action, Comedy, Fantasy, Slice of Life stuff. Not big on Horror (since I get scared pretty easily). More psychological stuff like Death Note is also really interesting to me.
But what really gets me more than the genre would be characters. If characters are interesting and well-developed I'll tend to like it more.
Mostly seinen I guess. Some shonen is cool but I like things a bit less over the top and more character-driven for the most part.
My tastes an anime/manga aren't really different from my tastes in media in general but I tend to lean more toward scifi, horror, and thriller type of shit I guess. I will say that I'm less into comedy anime/manga than I am western comedy, a lot of the humour in those just doesn't hit for me. I like horror moreso manga than anime, a lot of the better horror manga (anything by junji Ito, I am a hero, etc.) Tends to use really detailed realistic art styles that I don't think would really translate well to anime, and the art is a significant part of the appeal.
Edit: also I have a bit of a hard-on for cyberpunk tbh
Shounen, slice of life, comedy and some of its variations: dark because I'm a depressed shrimp that loves dark humour, and romantic every once in a while, but no one has to learn about it irl! Animes that revolve around psychology are a yes for me too, especially when I can relate to one of the character and/or can learn something.