There have been many players inducted to the Hall that have worn a St. Louis Cardinals uniform at one time or another. People like Dennis Eckersley, Orlando Cepeda, and Cy Young all played for the St. Louis Cardinals for a year or two during their illustrious careers.
To be in the seventeen inducted hall of fame players in this list, though, the player or manager must be a St. Louis Cardinal at heart, and have multiple seasons in the uniform. Moreover, they need to be inducted as a Cardinal: players like Stan Musial, Lou Brock, and Bob Gibson, or managers like Whitey Herzog and Tony LaRussa.