Quadcopters rely on computer stabilization to fly. They can be radio controlled, but with an onboard computer, why not let it fly itself? The community at DIY Drones developed the open source ArduPilot Mega (APM), an Arduino-based autopilot that lets you control multi-rotor (and other) aircraft autonomously, or via R/C.
The ArduCopter 3DR Quad Kit with Electronics includes everything to build your own quad UAV, except radio gear and batteries. Directions are easily downloaded, and assembly is relatively painless; just take care to put thread-locker on all screws, and balance the props. A wiki walks you through the Mission Planner software, firmware installation, and calibration of the APM board, sensors, and speed controls.
In autonomous mode, the ArduCopter takes off, follows GPS waypoints, and lands unassisted. In manual mode you fly it by the remote and make it hover (“loiter”) by flipping a switch. The DIY Drones community is there to help and they’ll push you to expand — add video or use a ground control station to wirelessly upload new coordinates — so you’ll never tire of your ArduCopter.