The biggest crisis in the Middle Ages in Europe was the Black Death. The Black Death reached Europe in 1347 and caused untold devastation. It is believed to have kiled up to half the population of Europe in just three years.
There were other crises that were more localized. For example, in parts of England, Ireland, and France, the coming of the Vikings was a major crisis. Viking raids and invasions killed and subjugated many people in those areas.
The Hundred Years war was another event that can be seen as a crisis for parts of Europe. This conflict was waged to determine who would dominate France. The fighting brought great hardship to people in the areas where the fighting occurred.