While the Concorde is (was) a beautiful plane (second only to the Spitfire in my opinion), it wasn't a real commercial success by any measure. Even with heavy subsidizies, the ticket prices were outlandish. The plane's limitations (short range, small passenger load, very high operating costs, no overland supersonic flight, etc) were largely determined by the 1960s technology used to create it. Unfortunately, even today's technology isn't up to the job of building a very high speed airliner that can economically viable.

Engine technology is probably the biggest limitation. There is hope, though, in that engine technology keeps progressing. Perhaps within 10-20 years, it will be possible to build a plane like that envisioned by Boeing's abortive High Speed Commercial Transport project from the 1990s. They were trying to create a plane capable of transpacific flights with up to 300 passengers. After years of research and a lot of money, they determined that the technology just wasn't ready for such a plane. The goal is to be able to create such a plane that could charge perhaps 20% more than a traditional 1st class ticket and make a profit. At that pricepoint, especially for the very long transpacific flights, they probably wouldn't have much trouble filling the plane.

As for some of the most significant planes of all time, I'd put the Spirit of St Louis on any list even over a design like the SR-71. The public excitement following Lindberg's solo transatlantic flight resulted in a tremendous boost to aviation.

I'd also recommend the plane that Jimmy Doolittle used to develop instrument flying. Being able to fly safely in bad weather is fundamental to military and civil operations.

Another contendor was the British de Havilland Mosquito, the wooden bomber/fighter/reconnaissance/anti-shipping plane of WWII. It was one of the most versatile designs of the era. For the same reason, I'd include the C-130. It has served in transport, gunship, special ops plane, drone mothership, maritime patrol, hurricane hunter, electronic warfare, rescue, and tanker roles, plus probably a few others that escape me at the moment. It has even been used to drop really big bombs like the Daisy Cutter.

AC-130 gunship
C-130/VC-130/LC-130 transport, VIP transport, Artic transport
DC-130/GC-130 drone carrier
EC-130 electronic warfare & C2
HC-130/SC-130 rescue
JC-130/NC-130 space & missile operations
KC-130 tanker
MC-130 special ops
RC-130 reconnaissance
WC-130 weather reconnaissance

Let's see, what others? I agree with Tom that the X-15 was very significant, as is the B-52. I'd probably include the Harrier because it was the first practical VSTOL design. You can't leave out the contributions of helicopters (even if some purists say they aren't "airplanes"). The Japanese Zero fighter gave them an advantage for the first year or two of the Pacific war and was a major influence on the development of American flighters like the F6F and F4U as well as fighter tactics. The B-47 was a ground-breaking plane that heavily influenced both bomber and future airliner/transport design. The U-2 spyplane was crucial in the Cuban Missile Crisis and soldiers on to this day.

This is fun. To me, an airplane hall of fame contendor should have a significant impact on aviation history, not just look cool, fly fast, or be produced in large numbers.