There are no provisions within the Code of Canon Law that permit for the pope to be fired or impeached from his position. According to church law, the pope holds the highest authority, which gives him full power in the Roman Catholic Church.
A pope may resign from his post, however, but he must do so freely and voluntarily. The last time a pope resigned was in 1415, when Gregory XII's resignation ended the Papal Schism, in which two men claimed to hold the title of Pope.
The Vatican is currently coming under attack in light of recent accusations that Pope Benedict XVI helped cover up incidences of child sexual abuse in the Catholic Church. Evidence has surfaced that while still an archbishop in Munich, Germany, Pope Benedict was included in a memo about a priest, who had been sent to therapy for pedophilia, returning to church work.
Some Vatican protestors are calling for Pope Benedict's impeachment, even going as far as calling for a criminal investigation into the matter. Yet, the pope is actually immune to prosecution under secular law and even the local laws of the Vatican.
In fact, the pope is even exempt from prosecution under customary international law, which protects heads of state from prosecution. As such, the pope is considered the head of the church and the head of Vatican City.