I cannot say what the Church says about a dowry or bride price, but I imagine these traditions are not practiced much, if at all in Europe, North America, and much of Latin America where such customs are pretty much things of the past. The only way we know of them is in literature and theater - such as in Grand Opera.
Today, these customs are still observed in parts of Africa, the Near and Far East… The Islamic world and India in particular; places where Christianity is very much in the minority. The only Christian Country I know of where these customs still exist is the Phillipines, and it is pretty much dying out there.