As the Pentagon is busy trying to control lightning, Wired notes that it's easy to download video from US warplanes and drones using a $26 app; see Not Just Drones: Militants Can Snoop on Most U.S. Warplanes and Insurgents Intercept Drone Video in King-Size Security Breach.
Wired also posted this 2002 video from CBS, showing an intercept in the act:
Update: there was a segment on The Rachel Maddow Show too, just the night before,
Update 2: According to the NY Times the Military Is Awash in Data From Drones. Newer drones are expected to record 10 directions at once, and many more in the near future, which should encourage research into storage, metadata, and organization.