An ornithopter is a machine that flies like a bird, by flapping its wings. Most orithopters are about the size of small birds. Larger, man-carrying models have been attempted, but so far without proven success. Airplane-sized ornithopters have accelerated to takeoff speed on a runaway, but full takeoff has never really been successful. The ornithopter was popularized in Frank Herbert's Dune book series, as well as in the recent movie Sky Captain and the World of Tomorrow.
Bird-sized model ornithopters are cheaply available and used by hobbyists worldwide. The ornithopter was first designed by Leonardo da Vinci and drawn in some detail in his notebooks. In lieu of feathers, it used a membrane, showing that da Vinci had some basic understanding of the mechanism of flight. It was meant to be man-powered, but did not produce enough lift to take off. The da Vinci ornithopter was likely never built.
The closest we have come to a large ornithopter is a project run by the University of Toronto, called Project Ornithopter. The ornithopter resembles a propeller prop plane, but lacks a propeller and instead has flapping wings. As stated before, it has been accelerated at takeoff speed down a runaway, but has not yet attempted full flight.
The first ornithopter was possibly built in Germany by Karl Friederich Meerwein in 1781 as a proof-of-concept for heavier-than-air flight. It is claimed to have flown, but more likely glided after being launched from a high place. When the aerodynamic principles of flight were elucidated mathematically in 1799 by George Cayley, it became obvious that gliders were more convenient than ornithopters, so much research in this direction was abandoned.
Some interesting projects have used chemically powered artificial muscles to flap the wings of small ornithopters. One day, robots like these might be used as imitation birds for surveillance. A benefit of chemically powered ornithopters is that they do not necessarily use combustion for power and thereby spare the sky from pollution.