It is very common for those attending confessionals or watching them portrayed on TV to hear the phrase say “x Hail Marys” or “x our fathers” at the conclusion of a confession. Where did this practice originate? Were other prayers or acts once more common?
This is a great question. In the early days of the Church, confession was practiced quite differently. It was done publicly, with the congregation present, and typically reserved for the very worst sins. It would be rare to confess more than once in a person's life. Penances were quite harsh, such as years of fasting or of being barred from reception of communion. One might even be give the penance of wearing special clothing for a period of time.
Irish monks developed the practice of private confession, which is now standard today, which proved far more popular. This let them also give more specific penances for individual sinners. There are examples of long books from this time period that served as manuals for priests to use when giving penances. This would develop into the genre of Handbooks of Moral Theology, which would list sins and their gravity (mortal/venial) and an appropriate penance. Given that even the illiterate knew the Our Father and Hail Mary, increasing or decreasing the number of these assigned was a practical way to give a doable penance that reflected to some degree the gravity of the sin.