The whipping you are probably referring to is the use of the discipline.
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The Church has not “banned” the use. What everyone else has said is correct and should be re-read carefully and slowly. But, to answer your question: some do still do it. I have heard of a couple religious communities that still do. Some members of Opus Dei do.
Opus Dei gave a good explanation on their website:
Why do they do these mortifications?
Penance and mortification are a small but essential part of the Christian life. Jesus Christ himself fasted for forty days to prepare for his public ministry. Mortification helps us resist our natural drive toward personal comfort which so often prevents us from answering the Christian call to love God and serve others for love of God. Also, this voluntarily accepted discomfort is a way of joining oneself to Jesus Christ and the sufferings he voluntarily accepted in order to redeem us from sin.
How important is mortification for members of Opus Dei?
For members of Opus Dei it plays a secondary role. The primary thing for any Catholic is love of God and neighbor. Penance and mortification aim to reduce our self-centeredness and so to help us to grow in love for God and neighbor. In keeping with its spirit of integrating faith with secular life, Opus Dei emphasizes small rather than great sacrifices, like sticking at your work when tired, being punctual, passing up a small pleasure in food or drink, or not complaining.
From how the website describes it the discipline does not cause great pain, bleeding, etc. like the movies make it out. They say it causes a little discomfort and that is all. I still think though that when it comes to penances these would be considered severe penances. I remember reading that there was a sister in the monastery with St. Therese who used to take the discipline frequently. St. Therese did not. She said that following the Constitution perfectly and happily was penance enough.
