I have just found this article about Christopher Reeve. Many others too. He achieved more than the vast majority of private pilots.
Some of the stories are interesting. Here in the UK, Winston Churchill MP (grandson of the famous one) had an FAA ATP, according to the US AOPA magazine a few years ago. Also the [in]famous Mark Thatcher reportedly kept a piston twin at Gatwick Airport, for which he must have pulled a lot of strings or it was many years ago!
Then of course there is Harrison Ford 
My favorite has always been John Travolta with, as far as I know, an ATPL license, the only privately owned B707 (which he flies himself), a business jet and of course his house which is more of an airport terminal (with a private runway) than a normal house.
Others on the list:
I can’t find any information about F1 drivers with pilot licenses, which is strange (I would expect almost all of them to have one).
Generally, not a bad company we have 
I wonder how many of those who are type rated on multi pilot aircraft are rated Captains. For private flights in FAA land you can do RHS on the SIC (second in command) rating.
Tom Cruise soloed the F14?
Vladimir wrote:
Tom Cruise (F14 of course)
F14 is boring, he went CPL(H) and logged 2000h on Airbus AS350 Écureuil sponsored by his new upcoming film and I tought Tom Hanks had a good deal logging ATPL simulator hours for free
Fyi, Kim Jong is claimed to have ATPL(A+H) but I don’t think via a skill-test route with an (alive) examiner
King Abdullah of Jordan. (Helicopters)
Peter wrote:
Tom Cruise soloed the F14?
I don’t think so, just a joke. He has a license though.
Peter wrote:
Tom Cruise soloed the F14?
Don’t think it was an F14, but many years ago we were both holding short of the rwy at KVNY and he definitely was in some kind of fighter jet. Sensibly, the tower controller cleared him for takeoff ahead of me – I guess he would have had a hard time slowing to the speed of the PA28 I was flying at the time ;-))
Otto Waalkes used to fly (not sure if he still is current).
Carlo Pedrosoli (Bud Spencer) was an acomplished ATPL and also rotary pilot.
Tom Cruise has a CPL and owns several biz jets as well as a P51 Mustang. I understood he also flies helicopters.
Sen. John Kerry is a CPL (SE/ME/IR).
George W.Bush had a CPL (SE/ME/IR)
Chris de Burgh flies helicopters as far as I know
John Travolta recently donated his 707 to an Australian Museum. It still has to accomplish the ferry flight however.
I understand that the Dutch King is also flying on regular KLM shorthauls as a FO
Richard Bach (writer – Jonathan Livingston Seagull) and Niki Lauda.
