My taste for anime is very broad, so I don't limit myself what I watch. Different genre requires different formula to become sucessful in my eyes.
I'll just name one general but important element, history. I want some if not full understanding of the main and supporting characters answering the 5 Ws. I don't want the anime fill with unanswered plot holes unless it is done with a reason. Background stories explaining events creating a more richer and bigger world for the story.
This won't apply to all anime, like Excel Saga or Shinobuden but yea basically no shallow characters and story.