I think it'll happen like this:
1. The US builds hundreds, then thousands of Global Hawks and derivatives to fight its air wars without risking aircrew. The technology grows.
2. Unmanned cargo carriage gets approval and widebody unmanned aircraft are developed for cargo applications.
3. The technology improves to the point where unmanned flight clearly becomes safer than piloted aircraft. The public is ultimately convinced.
How long will it take? I'd say 50 years or so. Pilots will be as obsolete as navigating by the stars. I don't like it. I don't want to see it happen. But the only way around it is if al-Qaida is successful in returning us to the 7th century.