I'd like to say I like all kinds of anime but I'm sure there are a few genres I haven't seen yet. Popular shows currently dominate my anime list, but as I dive into this world, I'm sure my list will become much more diverse.
I love shows with complicated stories and/or strong characters. I can get into any art style after a few episodes, and animation matters only during action scenes. Direction matters at all times, though.
Music is my reason for living and adds a whole new dimension to my watching experience. I have been known to enjoy series, that I would have dropped otherwise, because of the music. I love discovering music through different media so suffice it to say I love it when a show can introduce me to a new music genre.