How many times have the Minnesota Twins won the World Series?

Twice. The Twins defeated the St. Louis Cardinals in 1987 and the Atlanta Braves in 1991.

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Actually, 3 times. In 1924, as the Washington Senators/Nationals, the team beat the New York Giants in 7 games. This does count as part of the Twins history. To date, the Twins have won in 1924, 87 and 91. They also lost the 1925, 33 and 65 World Series.