The Catholic Register lists it as a biretta...see excerpt from recent article "During the consistory, each Cardinal knelt as the Pope placed on his head a red three-peaked hat, called a biretta. The Pope told them the colour was not only a sign of the cardinal's dignity, but also a visible reminder of their readiness to act with courage "even to the point of shedding your blood" in order to help spread the Christian faith."
It's called a galero (pl. galeri; L. galerum, pl. galera).
There is some confusion (see above), a Cardinal wears a red zuccehetto on his head most of the time, that's a small round skullcap. The biretta is the three peaked hat that a cleric used to wear from the entrance to the altar. A galero is a wide brimmed outside hat, and a mitre is the hat worn during services (over the zuccehetto) with the two tall peaks.