At the Sochi 2014 Winter Games, the Netherlands won gold, silver, and bronze in 4 different speed skating events:
Clearly, the Netherlands were a powerhouse in speed skating this year. Out of 36 medals total awarded in men's and women's (long track) speed skating, Dutch skaters took home 23 of them. They won at least one medal in every speed skating event, and won gold in both the men's and women's team pursuit events.
It is not all that unusual for one country to sweep gold, silver, and bronze in a single event. It happens on average perhaps once or twice per Winter Olympics. In addition to the four events listed above at Sochi 2014, the USA swept men's slopestyle skiing, and France swept men's ski cross. No country did it at Vancouver 2010, but it happened twice in Torino 2006, when the Austrians swept the men's slalom medals and the Germans took every medal in the women's singles luge.
It is also not unheard of for one country to sweep two events in a single year. The last time this happened was at Nagano 1998, when Germany took every medal in both women's combined alpine skiing and women's 3000m speed skating.
The Netherlands, however, is the first country to sweep four events in a single Winter Olympics.