In the Eastern Churches there is also one, equally contrite (and somewhat longer), recited by those who are about to take the Holy Communion, and who are properly prepared (fasted since midnight, prayed, confessed, and received absolution), but never in place of personal confession to the priest.
I must say, regretfully, that in some American Orthodox churches the practice of "mass communion" has crept into the praxis, where whole pews empty out to receive, and when it's obvious that all these people could not have confessed the night before, but are "riding" their last confession over and over, even though the priest always reminds that only (Eastern) Orthodox Christians who have properly prepared may approach the Cup.
This is not only a Roman Catholic problem. At the most recent General Retreat of the Society of the Holy Trinity (a pan-Lutheran Ministerium and Oratory) a paper was presented on the destructive effect upon Private Confession that is wrought by having an order of Confession appended to the Eucharistic liturgy.
www.societyholytrinity.org/2008gr-lehrke.htm
The abstract follows;
Corporate Confession and Forgiveness, although not a historic part of the ordo of the Mass, has after several centuries of use as a preparatory rite, come to be regarded by American Lutherans as an essential preparation for the Sunday liturgy. We need to consider the possibility that this post 16th century addition of another ordinary by which to lead the Sunday assembly to the Word of God is problematic in the celebration of the Gospel. Its use has eroded and supplanted the sacrament of Confession and Absolution, while it also presupposes the Mass, both the preaching of the Word and the celebration of the Eucharist. It advances the presumption that the human act of a general confession of sins and sinfulness can secure God's forgiveness, making the Mass virtually irrelevant.
A caveat to any who follow the link: Pr. Lehrke was extremely redundant in this presentation. Excellent points, but once they were made there was no need for repetition ad nauseum.
That would be The Confiteor. “Mea culpa, mea culpa, mea maxima culpa” is when the breast is struck.
Regards,