Confession in Buddhism
This is a good question; if the monks can confess their "sins", why can't lay people?

On the one hand, monastic confession is a product of the rigidity of monastic practice, which requires some formal means of realignment. But on the other hand, reaffirming one's determination to keep precepts is a great practice for all Buddhists. 

The standard practice for lay people in Theravada Buddhism to correct a broken precept is to simply retake the entire set of precepts (five or eight). There are standard religious formulae for this, so that might be a similar concept to a confession.

Beyond that, though, I think there is less need for Catholic confession since there is less sense of "sin" in evil deeds; since our concept of morality is utilitarian in the sense of "it's evil because it brings suffering", there isn't the sense of intrinsic "sinfulness" of a deed, and hence there seems to be less of the shame and guilt associated with evil in Catholicism.

So, the practical equivalent to confession in our tradition is probably just talking with a teacher about your problems; e.g., rather than confessing you drank alcohol, you would discuss your alcohol addiction or your view that alcohol brings happiness.