Let us all be quite clear about the 1870 Vatican I definition of Papal Infallibility: when the Sacred Council defined Papal Infallibility, it was a restrictive definition. The Fathers were not creating some new dogma from thin air, but rather clarifying an already held belief. It is essential that we understand this point.
I suppose that one could understand the basic motivation: the Pope in 1870 was the last hold-out of old-time monarchy. Those monarchs ruled by the theory of "divine right", in which it was believed that kings, by God's providence, had the right to sovereignty. This allowed kings to create a stigma about them, a cult of personality. This cult only existed in their country. Now imagine the pope, the head of the Church on Earth, the leader of most Christians in Europe, the conqueror of Napoleon, the conqueror of Bismarck (in each case, the Supreme Pontiff stood up to the politician, and in the end, the politician backed down). The Pope was loved in France, Italy, Spain, and Austria. The adulation that people doled out to the Pontiff led many to believe that the Holy Father was inerrant. Obviously, this is heresy. On the other hand, the increasing secular powers sought to denigrate the authority of the Church, through the relativist heresy. The definition of Papal Infallibility puts a stop to both heresies: know we know that the pope is only infallible in specific cases, and we know that Truth is, at the least, represented by the office of the Pope.
This restrictive quality about infallibility is based on four criteria. The first is the role the pope chooses to address the topic: he must be speaking as the Successor of Peter, the Supreme Pontiff, and Vicar of Christ. Second, he must be speaking to all Christians. Third, he must be speaking on a matter of faith and/or morals (not discipline, not prudential matters--like policy preferences). Fourth, his statement must be definitive, or final (not keeping the door open to future debate).
It is easy to see how these 4 criteria apply in the case of, say the definition of the Immaculate Conception or the Assumption. In each case, especially Ineffabilis Deus, all four criteria are made pretty clear by the Holy Father. Some have claimed that these two declarations are the only two infallible proclamations by a pope. This is a sort of "formulaic" approach to infallibility, that unless the Holy Father uses the exact formula that Pius IX used in 1854, it is not infallible. This approach is very convenient. It allows Catholics to play "Simon Peter Says" (stealing that one from Mark Shea...at least he's got a sense of humor), and cherry pick what they like from everything that Simon Peter's successor hasn't defined. Minimizing the extent of infallibility allows Catholics like Nancy Pelosi (supporter of abortion) and Sean Hannity (supporter of contraception) to claim that they are "ardent, practicing Catholics", yet reject a teaching of the Church. Their rationale is simple: "Simon Peter hasn't defined it, so I'm good!"
However, it isn't that simple. Nowhere in Pastor Aeturnus, Lumen Gentium, or even The Catechism of the Catholic Church is an exact formula spelled out. There are no magic words that guarantee infallibility. This means that any number of papal writings, speeches, or pronouncements can include infallible statements on faith and morals. A simple brush through history will identify several papal pronouncements that have each of the four criteria listed above.
1) Pope St. Leo I's Tome to the Patriarch of Constantinople, Flavius. In the Tome Leo definitivel and with finality declared that Jesus was fully God and fully Man, with two natures united, but not merged. When the Council of Chalcedon (called secretly by the Emperor to get Monophysitism approved) heard the letter, they immediately accepted it as the authentic Catholic faith, because it was presented to them by the Successor of Peter. Clearly, Leo was asserting his authority as Successor of Peter, defining a dogma with finality, for all Christians to believe as part of the deposit of faith. Hence, it is infallible.
2) Pope Agatho's letter to the Third Council of Constantinople. In this letter, Agatho defines the Catholic faith in regards to monothelitism to finally end the monothelite heresy. Here, the Pope writes as the Successor of Peter to definitely establish a doctrine of the Deposit of Faith for all Christians to believe. All four criteria are met: infallible.
3) Pope Paul VI's Humanae vitae. Fr. Brian Harrison, O.P. does a good job illustrating how Paul VI was clear that his decision on contraception (and abortion and sterilization) was to be taken as definitive and infallible.
4) Pope John Paul II's Evangelium vitae. In Paragraph 62, the Holy Father clearly references his role as the Successor of Peter, and declares that all acts of willful abortion are always gravely evil. This is due to Divine law and natural moral law, and it applies to all people. Can't get much more clear than that, can you.
The last two documents are rather interesting. You cannot make the claim that every declaration or statement in Humanae vitae or Evangelium vitae are infallible, and so you cannot make the claim that Papal Encyclicals are infallible. You can, however, claim that certain declarations in those encyclicals are.
