There have been many bad popes in the history of the Church. The list below is illustrative, not exhaustive. If you would like me to add more to this list, please e-mail me with corrections and suggestions; I would also be grateful for additional links to articles discussing this question if you happen to have them at your fingertips.
The teaching of the Church about her relationship to Jesus, [Incarnation|true God and true man]], risen from the dead and reigning in glory at the right hand of the Father, is that He acts to protect her from formally teaching untruths about faith and morals, the creed of the Church and the essential ethics of her members. For us, a man serves as the Vicar, representative, of Jesus; with us, he is a believer, just like us, who has received the Deposit of Faith from the apostles and their successors, the bishops.
The Church does NOT teach that men become sinless when, on behalf of Jesus and His People, he takes the chair of Peter and serves as the visible representative of Jesus on earth. "Infallibility," the guarantee that the pope will not formally teach error does not imply "impeccability," freedom from personal sins. The sad fact that Jesus has been betrayed in every age by men chosen to represent him does not dissolve the fact that Jesus stands guard over His Church, His Body, to make sure that she can never lead the flock astray in her official teachings.
The Pope is NOT like a pipeline to Heaven. The fact that we can surely and certainly judge that some popes have done what is evil, what is contrary to the mind of Jesus, shows that we have received His message in all its purity and that we can use His message to judge what is right and wrong. We can condemn the actions of the bad popes because we know the standards to which they should adhere. Their personal sins are their personal sins. They are not the sins of the Church. These popes, like all of God's children, will have to answer on Judgment Day for what they did with the gifts that GOD gave them. "Much will be required of the person entrusted with much, and still more will be demanded of the person entrusted with more" (Luke 12:48).
We cannot enter the Kingdom of Heaven by pointing out the sins of others. When we become conscious of the sins of the bad popes, we should do an examination of conscience about our own sins, and cast ourselves on the mercy of Jesus, who died to save us all.
- Not one of the bad popes attempted to change the teaching of the Church in order to excuse his sins. The adulterers, murderers, liars, and thieves could not teach that their actions were good. They never spoke ex cathedra (from the chair of Peter) to change any of the Church's teachings about faith and morals. Their behavior was evil, but Jesus prevented them from teaching that evil is good.
Pope John XII 955-963 Described by the Catholic Encyclopedia as "a coarse, immoral man, whose life was such that the Lateran palace was spoken of as a brothel, and the moral corruption in Rome became the subject of general disgrace." Pope Benedict IX 1032-1045 A murderer and an adulterer; the Catholic Encyclopedia admits he lived a "dissolute life" and was "a disgrace to the Chair of Peter." "One of the youngest popes, he was the only man to have been Pope on more than one occasion [three times!] and the only man ever to have sold the papacy." Avignon Papacy 1309-1377 The Avignon Papacy was the period from 1309 to 1377, during which seven successive popes resided in Avignon, in France, rather than in Rome. Great Western (Papal) Schism 1378-1418 A long series of Popes in Rome vs. antipopes in Avignon. Ended with the election of Pope Martin V. Sometimes as many as three people claiming to be the pope! Pope Sixtus IV 1471-1484 Allegedly erected a house of prostitution in Rome. (There are questions about this fact, specifically that the only real source for it comes from an early Protestant writer and hardcore anti-catholic... hardly unbiased evidence.) Established the Sistine Chapel. Unquestionably guilty of nepotism. Pope Pius II 1458-1464 Had two illegitimate children before he entered the clergy. Wrote some erotic works. Pope Innocent VIII 1484-1492 Had at least two illegitimate children before he became Pope. As Pope, he raised his children to positions of authority and wealth in the Catholic Church. Guilty of simony. Pope Alexander VI 1492-1503 Had at least four illegitimate children whom he then made rich through ecclesial appointments. He made his son, Caesar Borgia, a cardinal when he was only 18 years old. Caesar was an immoral and violent man who had his brother put to death as well as his sister Lucrezia’s husband. Pope Alexander held unspeakable orgies in his palace and kept mistresses who were married women. He died of syphilis. Pope Julius II 1503-1513 Had at least three illegitimate children before becoming pope.