Some near misses, human error was a major factor.
Windscale, UK 1957
"On October 8, 1957 a technician was heating up the reactor...... Because of the inadequacy of the temperature measuring instrumentation the control room staff mistakenly thought the reactor was cooling down too much and needed an extra boost of heating. Thus temperatures were actually abnormally high when at 11.05am the control rods were withdrawn for a routine start to the reactor's chain reaction. A canister of lithium and magnesium, also in the reactor to create tritium for a British H bomb, was probably the first can to burst and ignite in the soaring temperatures. This coupled with igniting uranium and graphite sent temperatures soaring to 1,300 degrees centigrade."
Brown's Ferry, Alabama 1975
"Two electricians were trying to seal air leaks in the cable spreading room, where the electrical cables that control the two reactors are separated and routed through different tunnels to the reactor buildings. They were using strips of spongy foam rubber to seal the leaks. They were also using candles to determine whether or not the leaks had been successfully plugged -- by observing how the flame was affected by escaping air.
The electrical engineer put the candle too close to the foam rubber, and it burst into flame.
The resulting fire, which disabled a large number of engineered safety systems at the plant, including the entire emergency core cooling system (ECCS) on Unit 1, and almost resulted in a boiloff/meltdown accident, demonstrates the vulnerability of nuclear plants to "single failure" events and human fallibility."
Three Mile Island 1979
"A minor malfunction, or transient, in the nonnuclear part of the system would evolve a series of automated responses in the reactor's coolant system, and during all of this, the relief valve on top of a piece of equipment called "the pressurizer" would become stuck open. Owing to continued misreading of the symptoms by the operators over a 2 1/4-hour period before the relief valve was closed and the turning off of an automatic emergency cooling system, the reactor core would become partially uncovered and severely damaged. It would be another 12 hours before the plant crew and the engineers from GPU Service Company would concur in effective corrective action. "
Tokaimura, Japan 1999
"The accident occurred when employees of JCO Co, the company which operates the plant, poured 35 pounds of uranium into a purification tank containing nitric acid, instead of the 5.2 pounds normally used. What followed was a flash of blue light inside the plant as the result of what has been called a nuclear fission chain reaction. The Tokyo Electric Power Company rushed 880 pounds of sodium borate to the plant to absorb the radiation emitted, but the workers had difficulty getting close to the processing tank"
The above four examples are just a selection, the list could easily have been several times as large.
When supporters of nuclear power can prove that power plants are immune to human error, then we can accept nuclear power as a viable energy resource. Of course they cann't, so we need to search for safer methods of energy production.
edit: typos