What are non-ordained lay person powers? According to apostolic churches (those claiming  apostolicity), what powers do the lay people unordained have?

For example, both the Church of Rome and the Anglican church agree that a lay person can baptise in an emergency: Emergency Baptism.

1284 In case of necessity, any person can baptize provided that he have the intention of doing that which the Church does and provided that he pours water on the candidate's head while saying: "I baptize you in the name of the Father, and of the Son, and of the Holy Spirit." (CCC)
What are non-ordained lay person’s powers?

Seeing that this is essentially quite a broad topic, this answer is being made into a community wiki response answer. 

Everyone who desires may add to the list. No one will receive points to this, not even myself.

Lay persons may have the following ordinary privileges or positions within the Catholic Church:


Servers at the altar 
Readers at Mass
Lay missionary
In modern times, ushers and readers are considered lay liturgical ministers 
Catechists who teach Catholic Christian doctrine


Lay persons in modern times fulfill various positions due to circumstances that present themselves in our modern times, with ecclesiastical approval, such as:


Eucharist Ministers due to lack of priests


In times of necessity or in a genuine emergency or in extreme circumstances, a lay person may also do the following:


Baptize someone in an emergency (near death) 
Baptize when no clergy is present in a region or country due to persecution and clergy or expelled from the area as in the persecution in Japan from 1614-1864.
Perform Catholic marriages when no catholic clergy is in the region or country (due to some possible persecution). This actually happened during a persecution in Japan from from 1614-1864.
Interpreters for a priest during confessions from one language into another. Such lay person’s actions carry the same obligations as a priest to guard to seal of confession forever.
Reading the Gospel and preaching in Catholic Churches and distribution of Holy Communion on Sundays in parishes, where there is a genuine lack of Catholic clergy to fulfill this need. This is not so uncommon in the “far north of Canada.” Lay persons are specially trained for this ministry. (The Sunday obligation in diverse regions is often transferred to another day due to particular circumstances and with Ecclesiastical approval.) This is common in the Diocese of Whitehorse (Yukon) for example.
Instituted Acolytes may function in the office of a Subdeacons (Extraordinary Form of the Mass) under certain conditions (lack of subdeacons). They shall however be denied the maniple. - Rome, June 7, 1997. Thus instituted acolytes of the Ordinary Form of the Mass may serve as subdeacons in Extraordinary Form of the Mass.