Only a comparative handful were built - and there have been no successors since the last flight in November, 2003. (The Soviet Union had a challenger in the Tu-144, but the design never really proved itself.) In contrast, Concorde achieved the distinction of simply being referred to as "Concorde", not "the Concorde" or "a Concorde". First flight carrying passengers on a regular schedule was January 21, 1976, on the London - Bahrain and Paris - Rio routes. Service to the U.S. didn't begin on a regular basis until 1977, as Congress had banned Concorde service because of public outcry over sonic booms. It took some maneuvering in the courts before the ban was finally thrown out.
With a genesis in the 1950s, a long development stretching into the 1960s and 70s, and a final flight with all being retired in 2003, Concorde's passing has left a hole in airline transport that has gone unfilled for the past 10 years.
More below the Orange Omnilepticon.
Concorde was all about speed - flying at Mach 2 (about 1300+ mph), it could make the transatlantic crossing between New York and London in a bit over 3 hours, compared with somewhere around 8 for conventional subsonic airliners. With a needle of a fuselage and swept delta wings, Concorde flew a unique course profile: get onto the assigned course track, go supersonic and cruise climb from 45,000 to 60,000 feet as fuel burns off. Friction with the air would heat Concorde so much, the airplane actually expanded in length by about a foot during the flight at cruise. There are military aircraft that can fly faster, but only the Blackbird or the XB-70 were designed to do what Concorde did: keep it up for hours at a time.
Flying so high (nearly twice as high as conventional airliners), loss of cabin pressure would have required pressure suits to keep the passengers and crew conscious; simple air masks would not be enough. (One reason for the small cabin windows.) The crew had positive pressure masks, but the main response would be to dive to a lower altitude as quickly as possible. Another effect of the thin air at altitude was somewhat greater exposure to cosmic radiation, mitigated by the shorter time in transit. Nonetheless, attention was paid to the possibility of solar flare storms!
In all the years of Concorde operation, there was only fatal accident. On July 25, 2000, Air France Flight 4590 crashed shortly after taking off from Paris, bound for New York. On take off, the aircraft ran over a strip of metal that had fallen off a DC-10 minutes before. A tire blew and fragments damaged the wings and underbody, leading to a massive leak of fuel and fire. All 100 passengers, 9 crew, and four people on the ground were killed. Normal Concorde operations did not resume until November 7, 2001 following improved safety measures and testing.
So, why did Concorde finally end up grounded in 2003, and why have there been no supersonic successors? There's no one answer - many factors combined to end the career of the Speedbird.
During the long development of the Concorde, greater speed seemed like the logical progression. Commercial airliners had been on a long track to fly farther and faster over the decades; going supersonic was the obvious next step. But... it was not enough. Concorde proved to be more expensive to build and operate than had first been expected - that was one reason why it only came to fruition as a joint Anglo-French project with heavy government backing. It's also why only a handful (20) were built - an expected batch of airline orders evaporated once the price became known. (And after the U.S. canceled its SST program, there are suspicions efforts to dampen SST enthusiams were pushed by the U.S. to protect U.S. airliner builders.)
There was (and is) a lot of opposition on environmental grounds. Fears of what a fleet of SSTs (Super Sonic Transports) would do for noise levels meant people already shocked by what the transition to jet airliners had done for people living under flight paths meant there was a ready opposition to SSTs in general. Further, there was concern what a fleet of SSTs would do to the Ozone Layer, given their much higher operating altitude.
At just about the same time Concorde began regular service, the Boeing 747 had already begun to change airline economics. Jumbo jets made it possible for the airlines to sell a lot more passenger seat miles on a given flight; Concorde had to fill 100 seats at a high price - and there were only so many people willing to pay a premium for speed.
Fuel costs did not help - breaking the sound barrier is expensive in terms of fuel - and increasing oil prices over the past few decades have grounded planes less fuel thirsty than Concorde as simply too expensive to operate. One of the supposed pluses for the Boeing Dreamliner is that its composite construction makes it more fuel efficient. The perilous financial condition of many airlines today and the depressed global economy also make operating something as demanding as Concorde unsupportable.
Finally, Concorde itself was becoming harder to keep operational. The small size of the fleet, the aging technology, the exacting nature of the spares - all of these factors led to the grounding of the surviving fleet in 2003. To the best of my knowledge, none are currently operable. A few examples are preserved: see here, here, here, and here. You can get a virtual farewell tour of the Concorde here.
So, a unique chapter in aviation history is receding into the past. Will there ever be another supersonic airliner? There are ideas that might solve the sonic boom problem. Novel engine technology might make higher speeds possible. But... it's hard to envision a market for an SST in a world where increasingly economic matters seem to conspire against bold visions - at least for people of ordinary means. Transpacific routes are perhaps the one place where such a plane might be viable - but no one is gambling on building one yet.
Some years ago I made my own transatlantic flight to England to visit friends. At the time, Concorde was still in service, and I got a glimpse of one at the British Airways terminal at JFK. It was unmistakeable; just sitting there it screamed of speed, glamour, elegance - all the things that seem to have vanished as air travel becomes ever more like an exercise in mass misery. The world is a different place from when England or France were just over 3 hours away, and one could dream of a flight to Australia or Japan on a next generation Concorde with the legs to make it in a direct flight.
One thing is certain. As the anniversaries of the first and last flights of Concorde fall further into history, there will be fewer and fewer people who will be alive to say they once flew faster than sound on a regularly scheduled airline flight, when mere mortals could aspire to realms now once more limited to the military, test pilots, and astronauts.