Until now the closest thing to flying like a bird was either hang gliding or open cockpit weight shift control aircraft. But now someone has solved the problems with one of the earliest designs for flying, flapping wings. A Dutch engineer has created a pair of bird wings for humans and video of his first flight is shown below. It appears there is some interesting gearing and motor assists and I would imagine some electronic control system, all the details are on his blog.
The general consensus developing is the video is a fake and I would have to agree. The give away is the pilots legs. At first they hang down, unsupported, but slowly rise and the pilot is stretched out. While early hang gliding harnesses suspended the pilot there were mechanisms for holding the legs extended. See this video for a comparison.
Update: The video maker admitted the hoax, an article on Wired Science has all the details.