Fr. Z was asked a question on what to do if you need a certificate for another sacrament, etc., and there was no record of it anywhere. (Read question and response here)
First of all, Baptism, Confirmation, and Holy Orders leave a mark on your soul, and therefore must be recorded. First Communion should be recorded for children, but it is not usually recorded for adults because they receive First Communion right after they are confirmed.
When I was in the Novus Ordo Church, my Baptism was recorded at one parish, and my First Communion and Confirmation were recorded at my most recent previous parish. My parents had to present my baptismal certificate in order to register for First Communion classes, which is a must. When I registered for Confirmation classes in the same parish church years later, I still had to represent my baptismal certificate from Parish A because SJ's did not record that I was baptized in Parish A! However, they recorded my First Communion, so I just had to give them an appoximate date (year) of First Communion so they could look it up in the register. Outsiders had to present BOTH certificates.
Please note that the parish where you were baptized is supposed to be notified when you receive a new sacrament or when you die, but I'm affraid this might not be the case, especially in Novus Ordo Churches, where some have adopted a congregational form of government.
This is going to affect me if I are to marry because I don't believe the parish where I was baptized exists anymore. While I have a copy of my certificate of baptism, Canon Law requires, in order to establish your freedom to marry in the Church, to have the parish of baptism give a recent copy (issued within 6 months) of the certificate.
So what do you do if the parish is closed? I hope they don't throw away the records.
Since I will marry someday in a Traditional Roman Catholic Parish, the priest may bypass this requirement since most N.O. parishes don't care about sacramental records, especially if a new presbyter comes in and deletes everything. Or in some instances, I might have conditionally receive Confirmation in the Traditional Rite in order to have a valid sacrament; not having received Confirmation is an impediment towards marriage.
It gets more challenging with SSPX or independent parishes because they may or may not accept certain certificates, or a diocesan parish may not accept an SSPX, FSSP, independent, or monastery baptism.
Even worse, if a layperson conditionally baptizes a baby using the proper Trinitarian formula because he is at danger of death and no priest is availiable, and if the baptism is not recorded on video camera, and/or you don't get the proper witnesses to testify that this happened, then is this hearsay? Where does a lay baptism get recorded?