The head priest of the Roman state religion was the Pontifex Maximus, or the greatest of the college of pontifices. While an obviously important and prominent position within the ranks of the Roman system, the Pontifex Maximus was not considered a magistrate comparable to a Consul, Praetor, etc.
During the Republic, the Pontifex was elected by the Comitia Tributa and served for life, while during the Empire, the position was generally held by the Emperor himself.
Originally, the Ponifices were Patrician only, but the social conditions and changes during the late Republic allowed for Plebeian election as well. These men were responsible for the oversight of the state religious cult as a whole and didn't really oversee particular godly cults, though they could if necessary.
By the Imperial period there were 16 pontifices under the high priest, 15 flamines, who were special priests of the main deities, and the Rex Sacrorum (king of the sacrifices) who performed the religious acts that the king had usually done. Perhaps most importantly, he was he was also responsible for the 18 Vestal Virgins.
The main duty of the pontifices was to provide the pax deorum, or the 'peace with the gods'. Interpreting omens, sometimes through augures, controlling and keeping the official calendar, and the oversight of funerals all fell under the domain of the Pontifex Maximus.
He was responsible for an enormous collection of omens (annales maximi); that would be recorded and collected on a nearly constant basis. These heavenly signs would be written down along with accompanying events, and used to determine the divine favor of the gods. Doing so allowed following generations of priests and magistrates to understand the historic will of the gods and interpret future events against past patterns.
Today, the head of the Roman Catholic Church, the Pope, is still called the Pontifex Maximus. It's a political or governing office that has been in existence and in perpetual use for nearly 3,000 years.
Did you know...?
Julius Caesar was elected pontifex maximus in 63 BCE and kept the office until his death. The house where he spent the night before he was killed, was the domus publica.