The standard rite of the Mass, which you see offered in church every Sunday, may be offered in Latin by any priest on his own initiative. The pre-Vatican-II Latin Mass, sometimes called the Tridentine Latin Mass, may be offered by a priest with the permission of his bishop.
Your bit of obscure Catholic trivia for the day: Priests who belong to religious orders that have a pre-Vatican-II Latin rite of the Mass (e.g., Dominicans, Carmelites, Carthusians) are allowed to offer their religious order’s Latin rite of the Mass without special permission.
