AMHR and ASPC have Hall of Fame; for this you earn points based on wins in regular, jr/sr and grand champion halter classes--there are point tables in the rule book--and to win a HOF award you need 5 Grands (with competition) and 70 points. You can earn points even if there is no competition, but in order for the Grand to count there has to be at least 1 other horse in the Grand Champion class. Same in performance--70 points and 5 Stakes wins. Again, point tables are in the rule book. If the division has no championship/stake class (jumper, hunter, etc) then you just need the 70 points. Horses can now earn multiple HOF awards in one division; not sure if that took effect this year, or not until 2012.
Then there are All Star awards--points are collected in each class and the horse with the most points at the end of each show year wins the award--certificates are given for champion & reserve all stars for each class listed. Points are collected even if there is no competition in the class.
Then there is Pony/Horse of the Year--there is a formula that is used to determine horse of the year but offhand I cannot tell you what that formula is--it is a bit confusing.