Ohhh, I've read a variety of manga's not adhering to a specific genre. A specific demographic maybe, but not so much genre. With me a good story is the deciding factor if I will read a manga or not. Good art helps but even if doesn't necessarily fall into the type of manga I usually read it doesn't mean that I won't read it. Here's a list of some of the thing I've read and loved over the years to give you a clearer picture:
Akumetsu, Hellsing, Bleach, Naruto, Vagabond, Death Note, Rurouni Kenshin, Rosario + Vampire 1 and 2, Fruits Basket, Hajime no ippo, Kimi no iru machi, School Rumble (made me lol very hard), Air Gear, Ouran High School Host Club(haven't finished it), Love Hina, Full Metal Alchemist, Angel Densetsu, Kekkaishi, Psyren, MX0, The Yagyu Ninja Scrolls: Revenge of the Hori Clan, XBLADE, Defense Devil, xxxHOLiC, and so on....
Manga adaptations I've liked: Shingetsutan Tsukihime, Persona 3, Persona 4
And of course Great Teacher Onizuka(one of my fictional character inspirations for wanting to become a teacher)
Manhwa's I've enjoyed: Girls of the Wild's, The breaker, The breaker: new waves
But the list could go on and on if I continued... : )
And you?