It all depends on the career, but as has been proven in the media and elsewhere, a woman's looks can impact her career even if she's in a job that doesn't rely on those looks. Like it or not, there is still a double standard that's alive and well in the world, and the work force is no exception. Business owners and hiring managers are patently aware that the average person doesn't really take issue with men who are balding, overweight, or have other similar appearance "flaws," but that people are much more likely to notice similar issues in women. While businesses can't use appearance as a reason for disciplinary action unless it was part of the terms of hire, that doesn't mean that doesn't influence it to some degree anyway.
That said, in my own career, I can safely say that my appearance has absolutely no bearing on it whatsoever...because I work online, and no one ever sees me.