Down thrust counteracts certain planes' tendencies to balloon as throttle (and speed) increases. On some planes, the Great Planes PT-40 for example, it can be quite drastic. Typically, a plane that has lots of down thrust will have a large wing with a flat-bottom or other high-lift airfoil. Aerobatic planes and warbirds tend to have smaller, symmetrical wings so the down thrust is less pronounced.

Sounds like the nitroplanes C17 fits the criteria of needing lots of down thrust, though.