The doctrine of papal infallibility means that the Pope cannot err or teach error when he speaks on matters of faith and morals ex cathedra.
They almost never speak Ex Cathedra. The last example of an ex cathedra decree took place in 1950, when Pope Pius XII defined the Assumption of Mary as an article of faith.
The Assumption is dogma.
Papal Infallibility has not been around long, not to be confused with the universal authority of the pope. Infallibility was defined at Vatican I.