Some of the biggest players in the world of commercial drones are drawing up plans for how to safely manage the growing flock of unmanned vehicles in what are quickly becoming crowded skies.

On Tuesday, Amazon.com Inc. laid out a proposal centered on slicing U.S. airspace into segments for different categories of unmanned aircraft, while keeping them all away from airplanes. The plan, described by Amazon’s top drone executive at a conference hosted by the National Aeronautics and Space Administration, would include one slice—a...