Anyone that is wise or sensible, wants to present themselves in the most positive light when actively going after employment, so that, there may be for certain people, an inclination to attach a picture to their résumé, especially if the perception is by doing so, that this will help them to get an interview for that job, and as much as interviewers want to tell us that they make decisions base on rational items such as experience, background, education, and so on, it just seems that when the initial introduction by a new applicant is done through a résumé, and that résumé has a picture on it, that picture will often influence matters, for better or for worse, no matter how much a particular interviewer denies it having done so.
While, in general, interviewers are not permitted to ask for or mandate a picture as a requirement in order to interview such, primarily because employers do not want to get on the wrong side of the EEOC, for insisting upon a picture in which requesting such places themselves in the unenviable position of having to justify how such a requirement does not violate age, race, or other discriminating factors, there is, on the other hand, the situation where the shoe is on the other foot, so that one's thought process should at least consider attaching a photo, of which, some people do, especially since they feel that they are going to be "outed" anyway, via social media, Google, LinkedIn or similar, so why not then get ahead of the curve and present typically the most conservative and professional looking facial photograph possible, in conjunction with their résumé.
Anyone that says that looks do not matter as regards to an interview, is not being honest, for in almost all situations, your look, will matter, at least to a minimum degree, if not more. This means, one should definitely consider adding a photograph onto their résumé, but should only do so, with the following caveats. The first caveat being that your look should be to the best of your ability, a look that you believe via the research that you have conducted a good representation of what you believe that the employer is looking for. The second caveat is that the photograph should be as professional as possible, typically conservative in taste, and strictly a facial shot from the shoulders on up. The third caveat is that if you are going to attach a photo to your résumé you may as well attach it to the top corner of said résumé, as opposed to the bottom or elsewhere, because that picture is your actual lead-in.
Then again, there are many reasons why a particular person would not want to attach their picture, which has a lot to do with an individual's perception of their look, and what it says about them, for a picture gives away one's basic race, one's gender, and one's basic age, all things, that may negate an opportunity for an interview, legal or not, so that all things being equal, prudence may dictate to skip the picture in the hope that a future face-to-face interview will provide you the chance to overcome snap judgments built upon your facial look to begin with.
We live in a world in which people claim that they make decisions just based on the facts, but, in reality, that isn't true, and most definitely how your résumé is structured, formatted, the words that you use, and what it says, makes a material difference on whether you get the job opportunity or not, so that the adding of a picture to such, does change the nature of your résumé, so that it very well might help you or hurt you, for as long as humans interview other humans, first impressions as done via a résumé, picture or not, matter.