There has been a large number of observatories launched into orbit, and most of them have greatly enhanced our knowledge of the cosmos. Many of them already completed their missions, while other are still operating. It follows a list of some of them.
NASA decided to undertake a programme that they called "Great Observatories".
The Space Telescope (ST), now known as Hubble Space Telescope (HST) is the optical Great Observatory. It was launched to great acclaim and soon after discovered to be flawed. Its main mirror contained imperfections in its grinding that resulted from a certain production limitation being accounted for twice. It has now been fitted with the equivalent of spectacles to compensate for this.
The Gamma Ray Observatory (GRO), since renamed to The Compton Gamma Ray observatory after several years of productive life had to be disposed of. Its gyroscopes began to fail and when it was down to its last gyroscope, the choice was to risk losing control or destroying the observatory. NASA ditched the bus-sized satellite into the Pacific Ocean in 2000.
X-Rays are also represented in the Great Observatories, with the Chandra X-Ray Telescope, renamed (from AXAF) in honor of the great Indian astrophysicist Chandrasekhar. This has been used to great effect to study distant galaxies and is still operational.
The fourth observatory its currectly called SIRTF (Space Infrared Telescope Facility, I think). It's an infrared facility, due for launch in several years' time.
Other notable space observatories are IRAS, which performed an all-sky survey in infrared, as well as discovering disks of dust and gas around many nearby stars, such as Formahaut, Vega and Beta Pictoris. This ceased functioning in 1982 and has since re-entered the atmosphere.
Hipparcos was a satellite for measuring parallax. Despite significant operational problems, it revised the Cepheid variable star distance scale to great accuracy and has been invaluable for all branches of observational astronomy by furnishing scientists with extremely accurate "standard candles" for measuring distances.