The Thoroughbred, Clydesdale, Shetland pony and Welsh pony. Can't think of many others that are really popular. Irish Draught to some extent, but not really that popular.
I'd say Shetland types or some sort of Welsh.
I say some sort since a skinny, badly built, TB-looking section C can be 14.2hh and still registered as Welsh.
Clydes and Clyde X's seem to be popular too.
Well, from what I've seen on my latest trips to the states.
Thanks everyone for your answers its just interesting to know, I know its not a native breed but I've heard hackney ponies are popular my friend has just imported 2.
The ponies I see over here are nothing like the sturdy natives you see in the uk. Most of them are bred to be fine boned and dainty now. Are halflingers british breeds? I see them advertised more and more.