Irving Penn has gotten to me a couple of times this way. Otherwise...no.
I teach photography at the university level. One of my favorite classes to teach is the introductory course in either film or digital photography. On the first day of class, when we go over the syllabus and I explain the arc of progress they will experience during the course, I tell them that about 20% of the class will do final projects that will move us to tears. They all laugh when I tell them that, but I reassure them that it will indeed happen and I make them a bet that it will.
During their final presentations, which are a 10 image essay that revolves around a single subject or theme. I push them to address ideas that tell us about them as a person, to explore what they really think and what they deeply care about.
Every term...and seriously I mean EVERY term, there are at least 4-5 students that move the entire class, myself included, to tears.
It is a wonderful thing to see these students grow and explore photography in a way that they were totally unprepared for. The first class to me represents the opportunity for them to set the stage for the type of photographer they want to be. I am very satisfied when they push themselves to the emotional edge and bring to the class images that are able to express their feelings and emotions.
I encourage this for those who have not cried when looking at photographs.
I think photographs have both an disadvantage/advantage when it comes to illiciting emotions.
Photographs physically reduce everything to a 2 dimensional piece of paper, so one's mind has to get around that impediment. A portrait of a deceased loved one can illicit emotions, but it isn't the photograph but rather the memory and sense of loss which the photograph triggers, and some photographs are better at triggering than others---it has nothing to do with craft---a faded and creased drugstore developed snapshot can be as powerful as a museum exhibition print.
Photographs are also (usually)trusted realistic representations and appreciation of genuine beauty is something that cuts across all cultures and will cause emotions to flow, although photography is often employed to the contrary creating illusions which cater to the animal, rather than intellictual appetite (advertising porn) which can stir strong enough emotions to buy a product, but isn't likely to draw any tears.
Photographs are perceived as honest, or not. I think this is has become a generational divide of sorts. Old tiers who come from a world where photographic proof was evidence of reality (so called "trick photograhy" being a curiousity and not taken seriously) versus the Photoshop generation where the "reality" is defined exclusively by someone else's imagination. Not wanting to start a controversy, but I don't think creatively Photoshopped compositions are likely to bring anyone to tears.
I think the last photographs which brought a tear to my eye was the one of the soldier's coffin with his dog beside it, and this-
My 2 cents anyway.
I steal time at 1/125th of a second, so I don't consider my photography to be Fine Art as much as it is petty larceny.
Only when I saw a photo of my grandfather taken on a British battle ship in WWII. I could have sworn I was looking in a mirror. I never got to meet him as he died of TB a year after the war.
A women cried when she saw one of my prints in a show in Japan. When she was a little girl, she used to stand by the stairs waiting for her dad to come out from his shift in the coal mine. He died in a massage explosion there in the 60's. So, photographs definately have the power to move one to tears. It was this image...
Often, I even cry at super market openings.