The greatest moment in Olympic history was when Michael Phelps won 8 gold medals at the 2008 Summer Olympics, setting numerous records in the process.
In his first race, the 400 m individual medley, he broke the world record in the preliminary heat, and followed that up by beating the record again in the final by almost 2 seconds and winning the gold medal
In his next race, he swam his leg of the 4x400 metre relay in 47.5 seconds, which was a new U.S.A record, and won his second gold of the 2008 Olympics.
For his third race, Phelps broke his previous record for 200 m freestyle race by almost a second and won his third gold medal of 2008. He also set his 3rd world record of the games, finishing the race in 1 minute and 42.96 seconds. He also became the fifth athlete in modern Olympic history to win 9 total gold medals at the Olympics (he won 6 golds in 2004.)
The next day, he participated in two finals. In his first race of the day, the 200m butterfly, he broke his previous world record by nearly a second and made it four gold medals at the games despite having his goggles filled with water for the last 100 metres and not being able to see.
Less than an hour after the butterfly race, Phelps swam the lead off-leg of the 4x200 m relay and won his fifth gold and set his fifth world record (Team record) by beating the previous record by more than 4.5 seconds.
Two days later, he won his sixth gold medal in Beijing by winning the 200 m individual medley with a world record time of 1:54.23.
The nest day, he won his seventh gold medal in the 100 m butterfly, with a world record time of 50.58 seconds and edging out the silver medalist Milorad Čavić by 1/100 of a second.
On August 17, Michael Phelps won his eighth gold medal of the 2008 Olympics in the mens 4x100 m medley relay, breaking Mark Splitz's record of 7 golds in 1972. Phelps and his teammates set a new world record in the event with a time of 3 minutes 29.34 seconds, which was 0.7 seconds faster than second placed Australia.
This is the greatest moment in Olympic history because Michael Phelps won 8 gold medals in 8 events, a 100% success rate. No one had ever done it before, and it will probably not happen again anytime soon, if ever. This was a very rare occurrence and an extraordinary feat for an individual.