How many types of rosaries are there?

The most common one is the Dominican rosary, it has been highly recommended by many popes, and by Our Lady, herself, in many of her approved appairations. There are other Rosaries approved by the Church including the Holy Trinity, Seven Dolors, Precious Blood, St. Bridget, St. Joseph, and the Rosary of the Lord. The Byzantine rosary is only used by some Catholic monks, not by lay-people.