The first pope of the Catholic Church was St. Peter, the apostle.
Since then (and including St. Peter), there have been a total of 266 popes in a continuous line of apostolic succession spanning almost 2000 years. The current pope (#266) is Pope Francis.
(FYI, if you find discrepancies in this official number sometimes, it’s because there have actually been 264 popes but 266 pontificates. Pope Benedict IX served multiple times, but with interruptions. So depending on how you count that, the number may vary. You also may see the total number sometimes put at 267, rather than 266. This is because they are counting Stephen II, who was elected pope, but died before being consecrated. He is not usually officially counted in the total number.)
An entire list of the popes can be found here.
Bonus: Listen to Why do we have a Pope?, by Scott Hahn.
As a former Protestant minister, Dr. Scott Hahn knows very well the common objections non-Catholics have to the Catholic Faith. In this informative talk, he tackles the tough issue of the Papacy and defends our belief that the Pope is part of Christ’s design for His Church.