Futurist John Robb has posted some interesting ideas on a concept called Dronenet, where he envisions a peer-to-peer logistics service using small UAVs. The primary constraints to this sort of idea taking off in the civilian sector are hardware and network standards, plus, some likely hesitance on the part of the general public to have quadrotors full of Chinese food deliveries zooming over their neighborhoods.
On the military side, we've seen a rudimentary version of a dronenet with the Marine Corps' apparently successful K-Max VTOL UAV logistics experiment in Afghanistan. During the 1990s, the K-Max was used by the U.S. Navy as a contractor-operator aircraft for vertical replenishment at sea. Every day, the Navy moves tons of ammunition, food, and other heavy stores via sling-load pallet from replenishment ships. While smaller, higher value - and time critical deliveries - such as circuit cards for weapons systems are often moved inside of helicopters. Could a network of smaller UAVs (with adequate range) handle VERTREPS in a more automated manner, speeding spare parts across the fleet, leaving the bulk stores for more traditional connected or vertical replenishments?