The Three Mile Island accident occurred on March 28th, 1979 at the Three Mile Island Nuclear Power Plant in Pennsylvania.  It was "the single most important event in the fifty-year history of nuclear power regulation in the United States".  Many people have seen the event as a turning point for the nuclear power industry in the United States. 
The Three Mile Island power station is near Harrisburg, Pennsylvania. The accident resulted in a partial core meltdown in Unit 2 of the nuclear power plant. Unit 2's pressurized water reactor was of 900 MWe capacity. 

The chain of events that led to the crisis at the TMI plant included several minor equipment failures that operator errors drastically compounded, resulting in a major accident. The Three Mile Island accident is largely seen as a failure of crisis management. According to one reviewer of the book:
 
Reactor operators were not trained to deal with accident conditions, and the NRC had not established effective communication with utilities. Moreover, once the accident occurred, the lines of authority proved to be ill defined. The public received conflicting reports that caused needless panic and evacuations. It was these systemic weaknesses in the regulatory system that allowed gifted people to make the mistakes they did.

Large portions of the TMI-2 reactor core melted, though the fact that a partial meltdown had occurred did not become clear until 1985. The greatest source of concern during the TMI crisis was a hydrogen bubble that formed in the top of the pressure vessel which held the core:
Although opinions differed, some reactor experts feared that over time the hydrogen bubble might become flammable or, less likely, explosive by combining with free oxygen in the vessel. If the bubble burned or exploded, it could rupture the pressure vessel and force the damaged reactor core into the containment building. The loss of the vessel would not make a breach of containment inevitable, but it would increase the risk of a disastrous release of radiation.

In the end, the Three Mile Island accident, though it "caused a grave crisis, did not produce a public health disaster". In the face of a core meltdown, the pressure vessel held and there was no breach of the  plant's containment structure. Only "tiny amounts of the most dangerous forms of volatile radiation escaped to the atmosphere". The TMI-2 cleanup took 11 years and cost about US$1 billion.

J. Samuel Walker suggests that the TMI accident incited widespread criticism of nuclear power technology, the nuclear industry, and the NRC. Critics faulted the industry and the NRC for their poor performance both before and after the accident. The international attention garnered by the crisis redoubled the determination of, and enhanced the credibility of, the anti-nuclear movement. Arguably, the United States nuclear industry has never recovered.

Walker reports that studies looking for long-term radiation effects resulting from the accident have reached conflicting conclusions, but it seems that any increase in cancers is slight enough to have occurred by chance.

Notes 

Nuclear accidents
March events
1979 in the United States
20th century in Pennsylvania
Harrisburg, Pennsylvania