1. Highest official jump: 8 feet, 2 inches
The red line marks the top of the obstacle. Image source
Officially, the highest jump achieved is eight feet, two inches (2.47 metres, or about 18 inches over Radar‘s withers) by Huaso and Captain Alberton Larraguibel Morales of Chile. The record was at Vina Del Mar, Chile, on February 5th, 1949.
Here they are on the other side:
The highest unofficial jump is eight feet, three and a half inches:
Fred (Freddie) Wettach, Jr. riding his horse King’s Own. They jumped in front of 25 people with motion picture photographers capturing the occasion. The record was not considered official because it was not made in front of a public gathering. Source
This page has lots more background information, and has a great animation of Morales and Huaso clearing the jump. As for me, I’ve always been a nervous jumper, and if I’m going to be that high in the air there’d damn well better be a flight attendant nearby.