A priest can say the New Mass (as of 1969/1970) in Latin without any formal permission from his bishop. However, this occurs even more rarely than the traditional Latin Mass.
A priest must receive permission from his bishop to say the traditional Latin Mass (pre-1969/1970). There is actually an ongoing debate as to whether this is necessary. But, the practical reality for now is that it is necessary to receive permission from the ordinary.
Catholics who love the old Mass, and the beautiful sacred music that usually accompanied it, have much to be optimistic about with Benedict XVI.
The Vatican has been more blunt recently in reminding bishops that they have the responsibility to allow or facilitate Latin Mass for those who desire it. A number of bishops -- and cardinals -- have shown a bizarre level of opposition toward allowing Latin Masses in their diocese. It really shouldn't be a big deal, and thwarting people for the sake of it has created a lot of bitterness.