What are some famous controversial photos that maybe shouldn't have been taken?

Nothing can beat the controversy that surrounded this photo.

This Pulitzer Prize winning photo is called: The vulture and the little girl, 1993.

It was taken by South African photo journalist Kevin Carter. Taken during the Sudan famine, this photo depicts a vulture waiting to feed on the corpse of the dying kid. According to Wikipedia:

In March 1993, while on a trip to Sudan, Carter was preparing to photograph a starving toddler trying to reach a feeding center when a hooded vulture landed nearby. Carter reported taking the picture, because it was his "job title", and leaving. He was told not to touch the children for fear of transmitting disease.
Sold to The New York Times, the photograph first appeared on 26 March 1993 and was carried in many other newspapers around the world. Hundreds of people contacted the newspaper to ask the fate of the girl. The paper reported that it was not known whether she had managed to reach the feeding center. In April 1994, the photograph won the Pulitzer Prize for Feature Photography.

Mentally destabilized by the very nature of this photograph and perhaps societal pressure, Carter couldn't enjoy the (de?)fame of this shot. He committed suicide on July, 1994. The story goes as follows:

On 27 July 1994 Carter drove his way to Parkmore near the Field and Study Center, an area where he used to play as a child, and committed suicide by taping one end of a hose to his pickup truck’s exhaust pipe and running the other end to the driver's side window. He died of carbon monoxide poisoning at the age of 33. Portions of Carter's suicide note read:
"I'm really, really sorry. The pain of life overrides the joy to the point that joy does not exist... depressed ... without phone ... money for rent ... money for child support ... money for debts ... money!!! ... I am haunted by the vivid memories of killings and corpses and anger and pain ... of starving or wounded children, of trigger-happy madmen, often police, of killer executioners ... I have gone to join Ken if I am that lucky."

There have been several photojournalists who have won the Pulitzer Prize after Carter, only very few of them shot a photo this harrowing.