Several people, both in my previous blog, and over on Amy's blog, have speculated that the availability of the Sacrament of Penance only in the face-to-face form is one reason for the decline in the use of the sacrament. I'm not sure about that, but what I am sure of is that the penitent should always have the option of going anonymously.
I've never encountered a confessional or "reconciliation chapel" which only permitted face-to-face confession, but gathering from your comments, such things must exist out there. If they do, they shouldn't. I quote from the relevant Canon:
Canon 964, s.1: The proper place for hearing sacramental confessions is a church or oratory.
s.2: As far as the confessional is concerned, norms are to be issued by the Bishop's Conference, with the proviso however that [emphasis added] confessionals, fitted with a fixed grille between the penitent and the confessor, always be available in an open place, so that the faithful who so wish may freely use them.
The canon makes clear, and I was, accordingly, taught in the seminary, that the penitent should always have the option of going to confession anonymously. Even at penance services and the like, when rooms not constructed as confessionals are put to use as such, I always arrange the priest's and penitent's chairs in such a way that the penitent can confess anonymously. It's simply the right of every Catholic to be able to do so at his/her discretion, not at the discretion of the priest.