That's tough, I'm open to all genres but if I'm not hooked in the first 10 pages I'll put it down.
My absolute favorite manga:
Mushishi: I love the slow pace and quirkiness of the premise, the main character is essentially a pest-control guy going around helping people with their problems, a lot of times not just with the pests, but also their interpersonal problems too.
Shaman King: This was the first real manga series I got into, and it still sticks with me to this day. I love all the different ghosts and human characters and how they interact. There's something about their deep partnerships that I really like.
Monster: Great story all around and the characters are memorable and engaging. And I love the deeper meaning behind those weird children's books and it was all together very intriguing.
Then I have a list of manga I was really into at the beginning but I will list the reasons why I stopped reading them (spoilers ahead).
Vinland Saga: It was really good and refreshing to see vikings, and the art and story were good but then suddenly the main character ends up as a slave and the tone of it all shifts, and the reader is not informed how he became a slave for a long time, I stopped reading before I even learned, still not sure if the author has told the audience yet.
Katekyo Hitman Reborn: I really loved this series, great characters, great action, great art, and great humor in the first few volumes, but then the future arc dragged on a little too long for me, and after I sat through that, the new mafia family they encountered didn't really do it for me. Then immediately when the new family misunderstood the Vongolas' intentions I stopped reading. I HATE misunderstandings that can be resolved with a simple sit-down and chat.
Naruto: Loved it in the beginning, got to around where Bee had his spotlight fighting, then the series got too long and got away from me.
So for me: plus points for an interesting premise and good characters; minus points for sudden tone shifts without explanation, dragging the story on too long, those damn misunderstandings, and writing something that takes 72+ volumes to complete.