One breed which comes to mind, is the American Saddlebred. Many seem to have a fixed idea that they are just high-stepping horses, suitable for nothing outside a show ring. So untrue. They make wonderful dressage horses and very good trail mounts, given the chance. Doesn't hurt that they are also beautiful.
A few years ago I would have added the Gypsy Horse/Cob/Vanner, but they have and are, still gaining a steady popularity, in spite of many who seem to wish to put them down at every opportunity.
I expect some of you who own different breeds, would like to 'sell' your own breed, to the horse buying public and tell why they shouldn't be overlooked.