I had an interesting thought the other day (I know that's rare but it does happen occasionally).
No one, while writing about the history of St. Louis baseball, has ever explored the idea of there being continuity between the 1875-1877 Brown Stockings and the 1882-present Browns/Perfectos/Cardinals. And in all honesty, the link is rather obvious and just sitting there.
In the fall of 1877, the NL Brown Stocking club collapses for various reasons-the gambling scandals, financial difficulty, the resignation of J.B.C. Lucas as president of the club, etc. A team is formed in 1878, also called the Brown Stockings, made up of a remnant of the Brown Stocking League club and playing their home games at the Grand Avenue Grounds. Organized by the Spink brothers and Ned Cuthbert (who had played with the Brown Stockings in 1875 and 1876), this club included Dickey Pearce, Lip Pike, Mike McGeary, Art Croft and Joe Blong, all members of the 1877 Brown Stockings. Same name, same park, most of the same players-the only difference between the 1877 Brown Stockings and the 1878 Brown Stockings was league affiliation and club officers.
This club, although not affiliated with any league, was a professional team that made road trips and attempted to compete on a national level. While almost certainly most of their competition was local, they did play clubs from Indianapolis, Louisville, and Akron. These Brown Stockings were also remarkably successful on the field. In 1880, they finished 20-1. In 1881, they also lost only one game. The 1881 team included Cuthbert, the Gleason brothers, George Seward, and Jumbo McGinnis, all members of the 1882 AA Brown Stockings.
It was the success of this club, combined with the relationship between Cuthbert and Chris Von der Ahe, that prompted the establishment of the Sportsmans Park & Club Association and the entry of the Brown Stockings into the American Association. Von der Ahe's Association club, then, was nothing more than the "semi-pro" Brown Stockings of 1878-1881.
So if the Interregnum Brown Stockings were nothing more than the remnants of the NA/NL Brown Stockings and the AA Browns were the Interregnum Browns placed in a new league then it's possible to say that rather than there being three distinct Brown Stockings/Browns teams in the 19th century, there was in fact only one team. League affiliation changed, club officials changed, players changed, the nickname changed but there is a continuity that extends from the 1875 Brown Stockings to Von der Ahe's Browns and therefore to the St. Louis Cardinals of today.
While the Cardinals celebrated there centennial in 1992 and most historians mark their beginnings in 1882, I think it's possible to argue that the history of the St. Louis Cardinals actually begins in 1875.