Wouldn’t one of the space shuttles have logged the most miles and hours, or is that not an aircraft?
Discovery, the veteran of the fleet, is NASA's oldest and most traveled shuttle. After 27 years and 39 flights, Discovery has logged 365 days — a full year — in space, and journeyed 148,221,675 miles (238,539,663 km). Over its career, Discovery also made 5,830 orbits of the Earth.
from:
http://www.space.com/12173-nasa-space-shuttles-miles-flown.html