Avatars with anime anything on them tend to rub me the wrong way, most likely because in my youth I spent a lot of time over at DeviantART. And oh god - the anime. I'm so tired of the anime. I even like some of the shows, but the fans... the fans I cannot abide. Too many obnoxious, drama-loving pre-teens.
I do though like to use avatars as a way of spotting potential friends or just cool-looking people. I do think you can tell a lot about a person by how they choose to represent themselves. So if I see a reference to a show, or comic, or music I really like, I tend to give that person's opinion a little bit more of my time.
Until, of course, I realize their opinion is stupid. Then I feel sad.