In Rome today, there are four archpriests, one for each of the four papal major basilicas; all of them are presently bishops :

Archbasilica of Saint John Lateran
Basilica of Saint Peter
Basilica of Saint Mary Major
Basilica of Saint Paul outside the WallsThe use of "archpriest" in the Latin Catholic Church  should not be confused with "protopriest", the senior Cardinal-Priest in the College of Cardinals. According to the specific historical tradition, many churches throughout the world, other than basilicas, are under the authority of a priest who bears the title of archpriest. However, the title is mostly honorary and today, such an archpriest has no control over subordinate clergy other than that of a parish priest over junior clergy assigned to assist him in meeting pastoral needs. In the  Latin Catholic Church, it was traditional in some localities for a priest to be assisted at his First Mass by another priest termed for the occasion the archpriest, who  functioned as the deacon otherwise does. This was not a permanent title but referred only to the particular occasion. Church of England
In the Church of England there is at least one archpriest, the Archpriest of Haccombe. The title is a survival of local  practice of Latin Catholic Church prior to the Reformation. It was first employed in AD 1315 and has been held ever since.
By the time of the Council of Trent the office of archpriest was replaced by the office of vicar forane, also known in English as "dean". The first recorded use of this meaning of the title comes from St Charles Borromeos reforms in his own diocese. Unlike vicars general and vicars episcopal, vicars forane are not prelates, which means they do not possess ordinary power. Their role is entirely supervisory, and they perform visitations for the bishop and report to the bishop or vicar general any problems in their territory. Exceptionally, the pope on occasion raised a territory to the rank of archipresbyterate nullius, detached from any prelature, yet under a non-prelate, as happened in 1471 with the future abbacy (1583) and later (1828-1986) Diocese of Guastalla. In the 16th and 17th centuries, during the persecution of Catholics in England, an archpriest was appointed by the Holy See as head of the Catholic Church in England, with authority over all of the secular clergy in the country.The title of archpriest has survived in Rome, in Malta and elsewhere, where it is now held by the rectors of the principal basilicas. However, the title is entirely honorary, reflecting the fact that these churches held archpriestly status in the past.