The Pope is infallible only when speaking "Ex-Cathedra" which literally means "from the chair." The doctrine of papal infallibility comes from the first Vatican Council (1870) and the pope has only used it once ... when proclaiming that the Blessed Virgin Mary was conceived without stain of Original Sin (the Doctrine of Immaculate Conception, not to be confused with the Virgin Birth).
I may be incorrect in this and please correct me if I'm wrong. The first Vatican Council simply defined papal infallibility. However, it defined than when speaking "ex cathedra" the pope in inerrant in matters of dogma concerning faith and morals. Infallibility was bestowed by Christ to Peter (and his successors), and thus has existed since the Resurrection; it was not simply "invented" in 1870. Therefore, while the Immaculate Conception has been the only pronouncement "specified" as being infallible, many other articles of faith (the Virgin Birth, Christ's divinity, the Resurrection, the Trinity) are equally infallible.
Pope Piux XII also proclaimed an infallible dogma - the Assumption of Mary.