What do you look for in an anime/manga?

I would have to say that story and character are the most important elements for me. Art is of course a very close second but I am able to look past odd or lower quality art if the story is engaging enough. Different art can be alienating at first, I recall the runner film on the animatrix DVD which at first I wrote off because the art weirded me out, but upon second viewing I was so engaged and moved by the piece that I actually came to love the unorthodox art. Music can be important but I find that many anime series use only few pieces of music to indicate certain moods/themes and merely repeat them perhaps with small modifications. Of course there are exceptions like Afro samurai which utilizes its hip hop soundtrack to great effect. For me the story definitely has to engage me first and the rest is bonus

I always look at whether or not I'll like the story. If the story isn't any good, no matter how awesome the animation or music is, it won't make up for a bad story.