On-and-On (April 24, 1956 – 1970) was an American Thoroughbred racehorse who was a top runner for owner/breeder Calumet Farm and the sire of their 1968 Kentucky Derby and Preakness Stakes winner, Forward Pass and the damsire of U.S. Racing Hall of Fame inductee Alydar. On-and-On died in 1970 and was buried in Calumet Farm's equine cemetery.