For the Amish certain holidays are observed by fasting. In the community I grew up in January 6th was the first day of fasting in the new year. We'd sleep in, and after getting up everything was somber, no singing, laughing, or anything fun. We were expected to sit and silently read prayers in our little black prayer book, or the rules of a Godly life.
At noon Mom and I would make breakfast, while Daddy read a few chapters from the Bible to everyone. Afternoons were much more fun, we could read for pleasure, play games, and anything else we would do on an in between Sunday.
Good Friday was the next fast day, followed by Ascension Day, and Whit Monday.
Twice a year the Sunday before communion was designated as a day of fasting in preparation to be considered worthy of partaking. A sort of cleansing any sin from your life.
Occasionally when the church hopes to intercede for someone that is struggling with something in their life they will ask for a day of fasting in hopes God will have mercy and change that person's heart and life.