Jesus' disciple Peter is considered by Roman Catholics to be the founder of the Christian church and the first pope. Protestants claim that documentation of this is very weak, and that in first few centuries of Christianity Bishop of Rome didn't have any special priviledges.
The Vatican Council 1869-1870 defined the dogma of papal infallibility where the pope, when he speaks ex cathedra, does not have the possibility of error on any matter of faith and dogma. All other Christian churches, and many Catholics, including even pope Paul VI (who said that he's never going to speak ex cathedra) reject doctrine of papal infallibility.
Whether someone was a Pope or Antipope is mostly matter of historician's own view.
See also antipope, sedevacantism.
List of all popes: