There are some companies out there that insist for resume with a photograph but most of them are happy without them.
We all carry some or the other like or dislike when it comes to looks and a photograph on a resume, promotes just that. Knowingly or unknowingly, a decision of accepting or rejecting the resume is likely to be made based on the photograph. If you are attractive, then it might seem that you are trying to impress with your looks which is unacceptable. The purpose of the resume is to highlight your professional skills and career progress. No point in shifting the focus.
Collating and editing the information is a herculean task. We are always short of space. In which case, a photograph does just that, occupies space which we would happily dedicate to some worthy content about your career.
A picture speaks 1000 words, make sure yours does not speak even one wrong word. That’s how particular you would have to be with your photograph when you are applying for a job. That’s where things get tougher. What is professional and what is acceptable is again an idea which varies with each company. If you still believe in having a picture on your resume, then it should be professional.
If you are applying for model or actor, then photograph(portfolio) is a must else it’s just not worth the risk.