Update (3:50 p.m. EDT): We don't get a happy ending to this one, unfortunately. The plane has sunk, according to the Associated Press. There's no sign the pilot survived.
Update (2:36 p.m. EDT): The pilot appears to be a doctor from Slidell, Louisiana, named Peter Hertzak, according to local broadcaster WDSU, which got the information from someone on the airport board in Slidell.
Update (1:26 p.m. EDT): There's hope for a happy ending yet. The Associated Press reports that "The plane landed softly in the water and was intact, floating right side up ... A Coast Guard helicopter was responding and a patrol boat was about 90 miles away."
Update (1 p.m. EDT): The plane, a Cessna 421 (an example of which is pictured above), is registered to Lee H. Aviation, Inc., of Wilmington, Delaware, according to Flightaware. It's a two-engine propeller plane, and the pilot was apparently the sole occupant.
Update (12:25 p.m. EDT): Breaking News is reporting the plane just went down 170 miles off the coast of Florida. (12:37 p.m.: CNN's Lisa Desjardins tweets that the Coast Guard confirmed to CNN the plane is down).
Original: The controls of an airplane might just top the list of worst places to lose consciousness. So we've got our fingers crossed for the apparently unconscious pilot of a private plane that's reportedly circling above the Gulf of Mexico, well off the coast of Florida, where he or she is expected to crash.