Armstrong had heart surgery several weeks ago, and a statement from his family said he died following complications resulting from cardiovascular procedures.
"Neil Armstrong was also a reluctant American hero who always believed he was just doing his job," his family said. "He served his Nation proudly, as a navy fighter pilot, test pilot, and astronaut. ... He remained an advocate of aviation and exploration throughout his life and never lost his boyhood wonder of these pursuits."
Read the full statement from Neil Armstrong's Family
On July 20, 1969, half a billion people -- a sixth of the world's population at the time -- watched a ghostly black-and-white television image as Armstrong backed down the ladder of the lunar landing ship Eagle, planted his left foot on the moon's surface, and said, "That's one small step for (a) man, one giant leap for mankind."
Twenty minutes later his crewmate, Buzz Aldrin, joined him, and the world watched as the men spent the next two hours bounding around in the moon's light gravity, taking rock samples, setting up experiments, and taking now-iconic photographs. The third member of their crew, Michael Collins, orbited overhead in the Apollo 11 command ship, Columbia.
"Neil and I trained together as technical partners but were also good friends who will always be connected through our participation in the mission of Apollo 11," said Aldrin today in a statement. "Virtually the entire world took that memorable journey with us. I know I am joined by millions of others in mourning the passing of a true American hero and the best pilot I ever knew."
Collins said, "He was the best, and I will miss him terribly."
President Obama issued a statement from the White House: "Neil was among the greatest of American heroes -- not just of his time, but of all time," it said. Armstrong and his crewmates "set out to show the world that the American spirit can see beyond what seems unimaginable -- that with enough drive and ingenuity, anything is possible."
NASA Administrator Charles Bolden -- himself a former space shuttle astronaut -- joined in the tributes. With the space shuttles retired, NASA does not currently have a way to launch astronauts on its own, but it is working on a new spacecraft, and, this month, landed the robotic Curiosity rover on Mars.
"Besides being one of America's greatest explorers, Neil carried himself with a grace and humility that was an example to us all," said Bolden. "As we enter this next era of space exploration, we do so standing on the shoulders of Neil Armstrong."
Armstrong's step fulfilled a challenge laid down by an earlier president, John F. Kennedy, in May 1961. Struggling in his first months in the White House, Kennedy addressed a joint session of Congress:
"I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to the earth," he said. "No single space project in this period will be more impressive to mankind, or more important for the long-range exploration of space; and none will be so difficult or expensive to accomplish."
Armstrong was a 30-year-old test pilot at the time of Kennedy's challenge, flying the X-15 rocket plane for a new government agency called NASA. He had served as a Naval aviator in the Korean War, flying 78 missions, and had an engineering degree from Purdue University. A native of the small town of Wapakoneta, Ohio, he was married to the former Jan Shearon and living near Edwards Air Force Base in the high desert of California.
NASA already had seven astronauts, flying its Mercury space capsule. In 1962 it sent out word that it was looking for more, and Armstrong was one of the nine it selected.
On March 16, 1966 he became the first American civilian to orbit the earth, commanding the two-man Gemini VIII mission with David R. Scott as his crewmate. On their fourth orbit, they made the first-ever docking in space with another spacecraft -- a maneuver the still-untested Apollo project would need to get astronauts to and from the lunar surface.
Minutes later, though, the spacecraft began to tumble wildly out of control, apparently because of a broken maneuvering thruster. It was a dangerous moment -- a 6,000-pound ship, moving at 17,500 mph, spinning and turning end-over-end once a second. Armstrong ended the emergency by using a second set of thrusters. Mission Control ordered the astronauts to land as soon as possible, and after 10 hours of flight they splashed down safely in the Pacific.
The two astronauts were commended for keeping their cool in a difficult situation, and when Project Apollo began, Armstrong was assigned to command one of the first six flights. At the time this was not momentous news. NASA had a system for rotating its crews among flights -- one served as backup crew for a mission and then actually flew three flights later -- and nobody knew how many test flights would be needed before the first moon landing could be attempted.
Armstrong, along with Buzz Aldrin and Fred Haise Jr., was named to the backup crew for Apollo 9, the third manned test of the new moonship. Soon Apollo 9 was swapped with Apollo 8 -- and Apollo 8 was then sent to take astronauts around the moon. The mission was a success. While it was still in progress, chief astronaut Deke Slayton took Armstrong aside and told him that he, Aldrin and Mike Collins would fly Apollo 11.
So it was happenstance that made Neil Armstrong one of the most famous names of the 20th century. If the order of flights had been different, or if Apollo 9 or 10 had run into trouble, Apollo 11 might very well have been a practice run for the first lunar landing.
But by May 1969 the rehearsals had gone well and Apollo 11 was next up. Reporters swirled around Armstrong. More than a million people crowded the Florida coast to see the liftoff.
"I think we're going to the moon because it's in the nature of the human being to face challenges. It's by the nature of his deep inner soul," Armstrong said at a preflight news conference, "We're required to do these things just as salmon swim upstream."
On the morning of July 16, 1969, Armstrong, Collins and Aldrin were woken before dawn. They suited up and climbed into the Apollo 11 command ship, high atop its 363-foot-tall Saturn V rocket.
Liftoff was flawless. Three days later the astronauts arrived in lunar orbit, and on the morning of July 20, Armstrong and Aldrin took their places in the landing ship Eagle, leaving Collins to run the command ship Columbia. They fired Eagle's main engine to slow themselves toward the moon's surface, aiming for a landing site on the Sea of Tranquility, a relatively flat plain near the moon's equator.
As they came in on final approach, Armstrong later reported, he saw they were in trouble. Eagle's computer was steering them right toward a crater, with boulders the size of cars. Armstrong took over manual control. Fuel was in short supply, but he hosed out more, skittering a few hundred feet above the lunar surface in search of a clear spot to land.
"1201 alarm," called Aldrin, watching Eagle's computer readout while Armstrong looked out the window. The computer was overloading.
"Hang tight, we're go," said astronaut Charles Duke, the one person at Mission Control assigned to talk with Armstrong and Aldrin by radio.
Armstrong was silent as he lowered the ship on a pillar of flame. He was too busy flying. Aldrin called out numbers to mark their progress in feet per second. "Four forward, drifting to the right a little."
"Thirty seconds," said Duke. In half a minute he would have to tell the astronauts to abort the landing -- even though they were less than a hundred feet up.
Finally, Aldrin called out, "Contact light" -- a signal that a five-foot-long metal probe, protruding from Eagle's landing legs, had touched the surface. The ship gently settled. Finally, Armstrong came on the radio.
"Houston, Tranquility Base here, the Eagle has landed."
Armstrong would say later that he considered the landing a much greater challenge, and a greater accomplishment, than actually walking on the surface. But after making sure Eagle was in good shape for the return trip, he and Aldrin put on their bulky backpacks and prepared to open the hatch.
It was 10:56 p.m., Eastern Daylight Time, when Armstrong backed down the ladder of the Lunar Module, went back up a step to make sure he could, and then planted his left boot in the lunar soil.
Armstrong walked on the moon for two hours and 21 minutes, Aldrin for about half an hour less. They took rock samples, set up two experiments, and took a phone call from President Nixon. They planted an American flag (with some difficulty; its staff wouldn't stand firmly in the lunar dirt and the flag itself, stiffened with wires, rumpled). They bounded around in the weak lunar gravity, reporting it was great fun but a little hard to stop.
Armstrong carried a camera, mounted on the chest of his spacesuit, and took some of the most famous pictures of the century. Aldrin did not have a camera -- so, in one of the ironies of the space age, almost all the still pictures from the Apollo 11 moonwalk are by Armstrong, not of him.
After a fitful night's sleep, the two men lifted off from the lunar surface and rejoined Collins in Columbia. They splashed down safely in the Pacific on July 24, 1969. They were greeted by ticker-tape parades and a beaming President Nixon. After that, Armstrong tried his best to resume a private life.
He served for a few years as a NASA manager in Washington. He taught engineering at the University of Cincinnati, not far from his birthplace. He served on corporate boards. He was appointed to the panels that investigated the Apollo 13 accident and the Challenger disaster. He declined almost all requests for interviews, and stopped giving autographs when people sold them for thousands of dollars.
A few personal details emerged: He suffered a minor heart attack in 1991. His wife Jan divorced him in 1994 and he soon married Carol Knight. In 2005 his authorized biographer, James R. Hansen, wrote, "Neil Armstrong today seems to be a very happy man -- perhaps happier than at any other time in his life."
Armstrong, who was born in the small town of Wapakoneta, Ohio, on Aug. 5, 1930, said he did not want to be an icon, remembered only for that one-week trip he made in 1969. He did appear at the White House to mark major anniversaries of Apollo 11, and when he did he urged America to go on exploring.
"There are great ideas undiscovered, breakthroughs available to those who can remove one of truth's protective layers," he said in 1994. "There are places to go beyond belief."
Editor's Note: This article was written and published on Aug. 25, 2012, the day Neil Armstrong died, and was updated this week with a new video to commemorate the anniversary of Armstrong's death. This update changed the time stamp on our mobile site, causing some to share the story on social media thinking we had published news of Armstrong's death today. We regret the confusion caused by the updated time stamp.