Shortest game lost on time
Ushinohama Satsuo 9-dan ran out of time after 51 moves against Yamabe Toshiro 9-dan in the 6th Tengen Challengers' Final on 23 October 1980 in Japan. Time limits were six hours each, but at the dinner break (from 5.30 to 6.15) Ushinohama, who had travelled up to the Nihon Ki-in from Osaka for the game, had only 51 minutes left. He did not turn up after dinner, and could not be found. It turned out he had fallen asleep in one of the bedrooms on the 8th floor of the Ki-in. As a result of this incident, which embarrassed the Nihon Ki-in vis-a-vis the Kansai Kiin, the bedrooms were put out of bounds.
Update by Alexander Dinerchtein:
Ushinohama has a very special playing style - he likes to create walls in fuseki, so we can often see him behind on territory. This game with Yamabe is a typical example. It's not yet over, because Ushinohama is a great expert of using such walls, so we cannot say that "He run out of time, because the game was anyway lost"
More info on that game, including possible continuations and pros opinions: