Beginning in 1920 a team that consistently won races had a hog, a pig, as their mascot. Following a win, they would put the pig (a real one) on the back of their Harley and take a victory lap A photo of the pig is also on their website. In 1983, an organization was formed, taking advantage of the long-standing nickname by turning "hog" into the acronym H.O.G., for Harley Owners Group.
Harley-Davidson attempted to trademark "hog," but in 1999 ultimately lost the case, with the appellate panel ruling that "hog" had become a generic term for large motorcycles, and is therefore unprotectable as a trademark. Thus the H.O.G. tradition began.