I’ve always valued a woman’s ability to empathize with others- from the people she knows, mankind in general, to all living beings in general. The wider this sphere expands, the more empathy she has, and I don’t mean “empathy” is some kind of hypocritical liberal hippie dippy way. I mean she’s genuinely able to feel how others feel and give sympathy and support when she can.
I personally value this quality more than anything else and consider it a key determinant whether someone is relationship material or not.
In a way, empathy is the other side of the same coin as seeing one’s own flaws and dealing with them well. Women who empathize are perceptive and easy to connect with. The prerequisite for these attributes is that they’re in touch and honest with their own emotions. Empathy for others also take a lot of compassion. I believe a person would not be able to give compassion unless she is capable of self-compassion. Someone who is in touch with her emotions and can be compassionate to herself is someone who can see her own flaws and deal with them well.
The opposite of empathy is solipsism. A solipsist generally exhibit narcissism, sense of entitlement, and isolation. They have a way of rationalizing away guilt, and use other people as a means to an end. Needless to say, solipsist women should be avoided at all costs. Unfortunately they are quite easy to find everywhere. Empathy is a rare quality.
I read Charles' comment on http://markmanson.net/one-trait and I agree with it. The ability to see things from another's perspective is very important.