David Letterman: Happy at Last After nearly 50 years of live broadcasting, he knows instinctively when a segment is about to run long. Normally, Letterman doesn't love talking about himself; what he wants to say, he says on his show. But today, he's sitting for an exit interview of sorts. A few weeks from now, at approximately 5:30 p.m. on Wednesday, May 20th, Letterman will wave good night, the lights at the Ed Sullivan Theater will go dark, and the Late Show With David Letterman will have taped its last episode. "For 30, 40 years, I was anxious, hypochondriacal, an alcoholic and many other things."