Right now there are several monasteries in Belgium that brew beer. These monasteries are all Cistercians, or more specific the Order of Cistercians of the Strict Observance, most popularly known as Trappists. The types that I've had so far are dark and rich ales. Recently an American abbey has teamed up with Sierra Nevada Brewery to make this liquid bread.
There are also some beers that had their origins in religious orders. Paulener wheat beer out of Munich used to be brewed by an order of Franciscans called the Minims. In Belgium there is Leffe beer that isn't brewed by monks anymore, but it's still affiliated with the abbey that started it.
I like beer, but a large percentage of beer's appeal to me is it's history, especially it's Catholic history. So when you find yourself looking for some brew, check out some Chimay, or try some Paulener Hefe-Wiessbier and relish in the though that some monk or friar had a hand in it's creation.
“From man’s sweat and God’s love, beer came into the world.” – Saint Arnold of Metz