Of course there are some exceptions. Most have to do with legally recognized regional names like Kolsch in the European Union.
And then there are Trappist beers. These are unique with the beer world. The "Authentic Trappist Product" label is a legally recognized however it is not about geography.
First, let's define Trappist. The Trappists are monks and nuns in the Order of Cistercians of the Strict Observance or OCSO. Their monasteries are found all over the world, on every continent except Antarctica.
Within the over 150 OCSO monasteries are the 16 members of the International Trappist Association which is, for lack of a better word, a trade organization. These are the only organizations that can carry the label. They make a wide variety of products from beer to shampoo which they sell to help pay for running the monasteries. Any extra money they make goes to charity.
Within the 16 member monasteries of the International Trappist Association, 8 brew beer as of this writing. In order to brew and sell beer, the monasteries have to follow certain guidelines. First, all the beer must be brewed in the monastery and by or under the supervision of the monks. The brewery must remain secondary to the monastery's mission. Finally, any money made by the sale of the beer must go to the living expenses of the monks or the upkeep of the monastery. Any extra money goes to charity.
Although the breweries within the monasteries are strictly monitored by the Association, they seem to have quite a lot of freedom regarding what the brew and how they sell it. Chimay in Belgium sells their Red, White and Blue beers all over the world. Westvleteren, on the other hand, only sells their beer on case at a time and only by appointment at their door. Achel makes four different styles of beer but only sells one. The other three are available only on tap at the monastery's guest house.
The styles brewed by Trappists are often associated with Belgian styles but that's really only because most of the monasteries are in Belguim. La Trappe is a brand brewed at the Koningshoeven Abbey in the Netherlands. Besides the usual Blonde, Dubbel and Triple, the brewers at Koningshoeven make Bockbeir and Trappist Witte, both unique among Trappist beers.