It is a big question, which there are many aspects of the law, which are still subject to debate today. I will try to answer based on my understanding of the law.
Constitutionally, anybody has a right to take any pictures in a public place, of what is viewed through his or her eyes, except, of course, some sculptures, building, or other things may be under copyright protection. This is a matter of First Amendment Freedom of Speech right, that Supreme Court will not hesitate to protect.
There are many exceptions. If the picture is taken of someone that he or she has a reasonable expectation of privacy, such as dressing rooms or restrooms, then the right is greatly diminished. If the picture is taken of some celebrity for commercial purposes, then the taker may be subject to an invasion of privacy lawsuit.
The biggest exceptions, however, are of and concerning children. Sexual explicit photos of children, even in private possession, will be prosecuated under various state laws and the Child Pornography Protection Act. This will include posting sexual explicit materials of one self.
Also, if the photo could be viewed in any aspect as defamational, then the taker may be subject to a lawsuit.
This is an over-simplied version of the law today and hopefully can put your dispute in rest.