Speedruns are completing a game as fast as possible under certain restrictions such as not being able to see. The main website for speedruns is Speedrun.com
Twin Galaxies has had a lot of talk about it. There was a speedrunner for the Atari game Dragster who was recently stripped of his records and got his world record taken away from him. He also had a Guinness world record taken away from him.
However, there is another, more infamous, more devious speedrunner. His name is Billy Mitchell. He set a bunch of records (he was the first person to apparently score over one million points) and actually was in a Donkey Kong documentary called King of Kong. However, there has been a bunch of evidence that he was cheating and the referee was actually the same guy who cheated at Dragster. Here's a video breaking down how exactly he cheated.