The ability to laugh at himself is the best short-cut method to knowing if a guy is balanced, confident, mature. I think this applies to women as well, but it is less a part of women's culture, so its absence may be less of a bad sign.
To laugh at yourself you need (some) insight, perspective, grounding in reality, self-honesty, confidence. It's not an infallible sign either way, as people can be able to laugh at themselves in some areas but not in others; there must also be well-balanced people who don't laugh at themselves, though none are coming to mind at the moment. I can imagine a type of person who is well but does not laugh at him or herself, but I can't think of specifics. Laughing at yourself is a sign of health. People who cannot are often brittle, easily offended by even the mildest criticism, self-important.
John McCain has some ability to laugh at himself; George Bush has a great deal. Hillary Clinton sometimes sounds forced when doing it, but I think at least some is genuine. Does anyone know of Barack Obama laughing comfortably at himself? I'm not picturing it, but I haven't seen a lot of him informally. It may be a very telling sign of his character.