A: 3 - The original Stanley Cup bowl was retired in 1970, and can be viewed at the Hockey Hall of Fame in Toronto.
It was replaced by a replica, which is currently the trophy presented to the winning team every spring and sent on tour with winning players.
Because the "new" Cup travels so much, the NHL had a second replica created in 1993. That Cup is on permanent display at the Hockey Hall of Fame.
So all told, there are three "official" Stanley Cups.