I think a lot of people have misunderstood the OP. They don't mean is it possible to fancy someone who doesn't fancy you, they mean is it possible to feel friendly towards someone who doesn't like you. Personally I don't think you can like someone who doesn't like you - you're automatically going to feel a bit resentful towards them, especially if they have no reason for disliking you. Then again, in a sort of hero worship type way, it can be possible.