The Rockies draft picks started to become a bit more successful starting in the 2011 season. In 2011, they had two first round picks, the 20th overall and the 45th overall (the second of which was compensation for losing reliever Octavio Dotel via free agency).
The Rockies chose left-handed pitcher Tyler Anderson and shortstop Trevor Story for those two spots and, obviously, both are key pieces for the Rockies now as Anderson is one of the Rockies starters and Story is the Rockies shortstop.
Some of the other players following Anderson in the first round include:
Joe Panik: 29th overall, 2015 MLB All Star
Jackie Bradley Jr.: 40th overall, 2016 All Star
Michael Fulmer: 44th overall pick, 2016 AL Rookie of the Year, 10th in the AL Cy Young Award voting in 2016, 2017 All Star
Others that came in later rounds include Mookie Betts (who, by WAR, is the most successful player in the draft at 28.1. He also has two All Star appearances, ranked in MVP voting twice including a second place finish in 2016, one Silver Slugger Award, and two Gold Glove Awards) , Ken Giles, Travis Shaw, Cody Allen (for the second time, both by the Cleveland Indians).