The 1871 college football season is the only year since the first season in 1869 in which no games were played.[1][2]
Princeton did play several games against a Princeton Theological Seminary team in 1871, although the Tigers considered these "practice" (or exhibition) games, and the general convention is not to count these as official games.[3][4]
Because no games were played, 1871 is the only year since college football play began in which no college football national champion has been named, retroactively or otherwise.