Jason Varitek: drafted by Minnesota Twins in 1st round (21st overall) in 1993 but did not sign.Varitek was again taken in the first round in 1994, 14th overall by the Seattle Mariners this time, and went on to have a 15-year career in the major leagues. He was a three-time All-Star, won a Gold Glove and Silver Slugger Award, and won a pair of World Series with the Boston Red Sox. Photo: Tim Umphrey, Getty Images