Discussion: What Makes a Compelling Character

Since there have been so many discussions on character development (male, female, or otherwise) I wanted to start a discussion (just a discussion here, no promises implied) about what it is that you find the most compelling or interesting about a character? What is it that makes a strong female character strong, or a male character the right kind of vulnerable? What is "enough" for the development of a character?

Everyone has their different perspectives and rather than an argument about what people don't like, I thought it would be productive to find out a bit more about what it is you like.

(Examples are always welcome as well.)

*As always, please keep it clean and refrain from any personal attacks or inappropriate discussion. Please avoid flame bait points of discussion. ie. If you know it usually ends badly, please try to be aware of that.

I see a lot of people say that they want a character that's written without gender in mind, but even when this is done, gender defines the character, at least it does in your mind. Thus, there are expectations of that character based on that. i.e. As I mentioned before, Jaina going after vengeance to some makes her "crazy".

I also see a lot of vague mention of "relate able" or "realistic" or "rational". What makes a character fit this, and how do you think this translates into the game (within the restrictions that it entails.)?

(I'm just pushing the conversation a bit further here. Thanks to everyone who's participated so far. Very well thought out posts.)