SR-71 Blackbird was crossing the control-zone of London Control. Evidently the controller didn't know the service ceiling of this aircraft is around 30,000 metres (yes metres, not feet!). There are so many variations on this item that the original event has evidently become part of aviation folklore or joke-lore.
Pilot: "Radar, Good Day, Airforce Blackbird, request FL 600(!)"
Controller (amused): "Sir, if you can reach, you are cleared FL 600"
Pilot: "US Air Force Blackbird, leaving FL 800, descending Level 600..."
"There were a lot of things we couldn't do in an SR-71, but we were the fastest guys on the block and loved reminding our fellow aviators of this fact. People often asked us if, because of this fact, it was fun to fly the jet. Fun would not be the first word I would use to describe flying this plane. Intense, maybe. Even cerebral. But there was one day in our Sled experience when we would have to say that it was pure fun to be the fastest guys out there, at least for a moment. ..."
That's high for a large body airliner, but some smaller business jets can go higher because they have better aerodynamics and engines. Service ceiling figures from wikipedia:
Gulfstream 550 and Dassault Falcon 7x: 51k
F14, F18, B52, and B-2: 50k
F15, F16, F35, B-1B, Su-47: 60k
F22, Typhoon, and PAK FA: 65k
U-2: 70k
SR71: 85k
A380, A350: 43k
A340, A330: 41k
A320: 39k
Boeing 787, 777: 43k
Boeing 757, 727: 42k
Boeing 747-400: 41k
Boeing 737: 35k
The 85k for the SR-71 is the unclassified information that has been made available. Rumor has it they hit 100k+ with the SR-71. Figures on actual ceiling for the SR-71 flights that were made have never been made public.
I don't know what you mean by "planes." All airfoil based aircraft have a limitation on how high they can fly before the air gets too thin for their wings to generate sufficient lift (known as their "operating ceiling").
The only exception to this I know of would be a craft with enough thrust to use power as the source of lift (like the space shuttle).
