An
aircraft built primarily by its intended
owner/
pilot. The FAA classifies these aircraft as
experimental, as long as the
owner/
pilot puts in at least 51% of the building time. Many companies that make these
kit planes push that rule until it scream with "quick-build" kits.
Since the trial lawyers bled the production side of general aviation nearly dry in the 1970s and 1980s, all of the innovation and entrepeneurial spirit in general aviation has been on the home built side of the ledger. The result is dozens of interesting an innovative designs, such as the Long-EZ, the Berkut and the Velocity, and many reproductions of classic aircraft, including dozen of WWI and WWII warbirds, the Beech Staggerwing (as the Lionheart), and others.
Just to respond to scytale's point, general aviation is generally pretty risky. Small aircraft are neither as redundant nor as tough as commercial airliners. The pilots are also not as skilled or experienced. General aviation pilots are aware of these risks and choose to take them. Flying is a hell of a lot of fun; flying an airplane that you crafted with your own hands is said to be an even bigger kick (can't say for sure myself yet). And there's a reason it says "EXPERIMENTAL" inside the door when you climb into a homebuilt. Only reason you've heard of that accident is because John Denver was famous.
I also went and read the NTSB accident report for that crash. Turns out that John Denver violated the First Commandment of Piloting: Thou Shalt Fly The Fucking Plane. His engine cut out at 400 ft due to fuel starvation, and he ceased to fly the plane to fix the fuel situation. He then accidently kicked the rudder pedal, sending the aircraft into a steep dive, resulting in his death. If he's followed the first commandment and set up for a water landing, he would probably still be alive, with another war story to tell.