I finally succumbed and purchased an inexpensive camera drone, and am posting this "first flight test" as a way to show potential quadcopter purchasers what to expect. Quadcopters are probably the most popular form factor for the current crop of consumer drones.
The one I purchased is an L6056, it's inexpensive (less than $50 on Amazon) and small enough not to require FCC registration. It comes "ready to fly", meaning you get everything you need except the four AA batteries for the transmitter (the remote control pad). It even comes with a 4GB memory card for the camera.
The original video actually looks a little "sharper" than shown here, as YouTube does some conversion/compression that affects it a little. The video is nothing special, it's simply my first brief outdoor flight with this new drone - but there are a couple of things that may be helpful to note.
First, the video quality is actually pretty good for a cheap drone - there is only a moderate "jello" effect (a visible "wobbling" of the video), which is one reason that I purchased this particular model. The video is only 720p - the low end of "HD" - but in good light the quality is more than acceptable for my purposes.
Second, this drone does not have a "gimbal" for the camera mount, something usually found in more expensive drones; the camera just attaches to the underside of the aircraft.
You will notice in the first video that any corrections I made in the flight are visible in the video (the video tilts and shifts, especially near the end), where a gimbal would allow a much smoother, more stable image with little or no extraneous movement.
Having said that, if you fly on a calm day you can often get decent periods of smooth video if you don't have to keep correcting the quad's flight. Some judicious after-the-fact editing may help too.
You can also "cheat" to some degree by uploading your video to YouTube and using the stabilization tool they offer, although that is not a panacea and can degrade the video quality a little more. See below (I also added some royalty free music courtesy of YouTube).