The Hubble, the most famous of all telescopes, has sent a steady diet of spectacular space images back to Earth since it was launched in 1990.
It has been invaluable in helping astronomers and astrophysics understand how the universe was formed and how stars are born and die.
The Hubble could malfunction at any time, but NASA predicts a failure between early 2006 and 2008.
At some point after that, a robotic ship will be used to push the satellite out of orbit and it will burn in the Earth's atmosphere.
A shuttle mission targeted for mid-2005 would have repaired broken gyroscopes used to aim the Hubble and astronauts would have replaced batteries that are working on borrowed time.
That mission, now cancelled, would also have new instruments, including the Wide Field Camera 3, powerful enough to see back in time to the period when the first lights in the universe turned on.
"Its early termination and the failure to deploy the sort of last generation of instruments is tragic. The loss is immeasurable"
Because of the time it takes light to reach Earth, telescopes as powerful as the Hubble actually act like time machines, allowing scientists to peer at the universe as it was billions of years ago.
"Its early termination and the failure to deploy the sort of last generation of instruments, which were even more fully able to exploit its capabilities, is tragic. The loss is immeasurable," said astronomer Donald Hall of the Institute for Astronomy at the University of Hawaii.
The space agency's decision, announced by NASA Administrator Sean O'Keefe to scientists and engineers at the Marshall Space Flight Centre in Maryland, where Hubble's mission is managed, was a direct result of safety concerns after the loss last February of the space shuttle Columbia.
The announcement came on Friday, the anniversary of Columbia's launch on a 16-day science mission that ended in disaster when the shuttle broke apart while re-entering the
New safety requirements put in place following the Columbia Accident Investigation Board's stinging rebuke of the shuttle programme's management and culture make it hard to launch a shuttle anywhere except to the International Space Station, where the crew could remain, awaiting a rescue mission, if the shuttle was damaged.
"Tying up two shuttles wouldn't work with the construction schedule for the international space station"
A Hubble mission would have required launching one shuttle and having a second on standby, ready to launch if a rescue was needed, said NASA spokesman Al Feinberg.
"Tying up two shuttles that way wouldn't work with the construction schedule for the international space station," he said.
NASA has plans to launch another space telescope in 2012, but astronomers expressed concern that funding for many projects will dry up in the intervening years.