Accountability. A person should own his actions, good or bad, and never throw up his hands to say that he's helpless or there's nothing he can do to better or change his life. Thinking you're not in control of your own life is the beginning of a downward spiral.
I think the most important quality every person should own is good self-worth. Without it, there would be depression, self-doubt, and inner turmoil. In having good self-worth, there is a sense of inner peace and well being which can be felt by others.
I think the most important quality is control your anger for the first 30 seconds. If it is controlled then it is almost gone. At least then your mind restores the rational aspect over the emotional one.