I've tried multiple anime titles throughout the years: Akira, Ghost in the Shell, Deathnote, etc... I really just cannot get into this style of animation. I love that many of the studios still use traditional animation practices, and enjoyed Ponyo and that movie with the little girl and the black gooey demon that rejurgitates gold coins, but so many of them make me sleepy. It's not the foreign dubbing that bothers me (I watched and loved Epitafios) or the animation style (like I said I enjoyed other similar products on a short term) but something about the genre just bores me silly....
Anime isn't a genre, it's a medium. There are many genres of anime.
If you don't like the art style then it's probably just not for you, since that's one of the main draws.