There are a lot of stars in the sky, and most of them are not named. With telescopes, we can see many millions or billions of stars, and it is impractical to name them all. Many schemes to uniquely identify stars have been proposed historically. In the early days, stars that were particularly bright or considered significant in some way, were given names. However, this system ran into trouble because there are just too many stars. With the naked eye, we can see around 6000 stars in the night sky under the best observation conditions (about 2000 visible at a time without turning the head).
Some of the brightest stars in the more prominent constellations, have proper names. For example, Orion has several named stars, including Betelgeuse, Rigel, Bellatrix, Meissa, Saiph, Alnitak, Alnilam, Mintaka, Algiebba, etc. (the fact that several of these names sound Arabic should come as no surprise).
The next step was to give them names based on the constellations in which they occur (Bayer Designation). Greek letters were chosen, so for example, stars in the constellation Eridanus can have names like alpha-eridani, beta-eridani, kappa-eridani, etc.
This system isn't so great either, because there are only 24 letters in the Greek alphabet, and constellations can have many more than 24 stars. Initially, Bayer extended this system by adding the English alphabet to the Greek, thereby having 24 Greek letters, 26 English letters (a-z) and 17 uppercase English letters (A-Q), making 67 in all (uppercase R-Z were reserved for variable stars). Obviously, 67 isn't enough either, so other systems were proposed, such as doing away with letters and using only numbers (Flamsteed Designation), so you can have stars names like 68 Eridani.
None of these names really ever went away, so today stars can have multiple names. For example, the brightest stars in Eridanus have proper names, such as Beid, or Zaurak. But Zaurak is also gamma eridani according to Bayer, and 34 eridani according to Flamsteed. Or it can be HIP18543 according to the HIP catalog, or TYC5311-1285-1, or something else altogether, depending on which catalog or nomenclature you follow.
Star Catalogs were first used to compile lists of stars by the Chinese, and soon after by the Greeks. Wikipedia has a nice entry on the history of star catalogs. Some of the more popular catalogs in use today include:
The TYC and HIP catalogs
The European Space Agency launched the Hipparcos satellite in 1989, and its mission lasted for 4 years until 1993. Hipparcos was an astrometric satellite, and its job was to provide high accuracy measurements of stars [Hipparcos is an acronym for High Precision Parallax Collecting Satellite, specially chosen to sound similar to Hipparchus, the ancient Greek astronomer and mathematician from around 150 BC, who charted many stars]. Lots of information about the Hipparcos mission and data can be found at the ESA site here.
The Hipparcos satellite had two main instruments: the Hipparcos instrument, which measured 5 parameters for about 120,000 stars with high precision, and the Tycho instrument, which measured another few hundred thousand stars with somewhat less precision and with 2 color spectrophotometry. This resulted in two catalogs:
The Hipparcos Catalog: contains the position of about 118,000 stars with 1-3 milliarcsecond accuracy, plus other data regarding variability, binary/multiple star systems, etc. Limiting magnitude was about 12.4, and the catalog is complete to magnitude 7.3.
The Tycho Catalog: contains 1.05 million stars with position data at about 20-30 milliarcsecond accuracy, and 2 color photometric data. There is an expanded Tycho-2 catalog (based on exactly the same data as the original Tycho catalog, but using more modern methods for computer-based image analysis), which contains about 2.5 million stars (99% complete to magnitude 11, 90% complete to magnitude 11.5). The data is also slightly more accurate than in the original Tycho catalog.
These two catalogs (Hipparcos in particular) have a special importance because they are contain space-based observations, which are several times more accurate than ground-based observations. Their one drawback is that data on the proper motion of stars isn't very good. The satellite was in place for only 4 years, which isn't a very long time to make observations of proper motion. This was somewhat remedied by combining the Tycho data with the much older Astrographic Catalog, into the combined ACT data set.
The USNO-B1.0 Catalog
This is a huge catalog, containing over a billion stars, compiled by the United States Naval Observatory. The data were obtained from scans of 7,435 Schmidt plates taken for the various sky surveys during the last 50 years. USNO-B1.0 is believed to provide all-sky coverage, completeness down to magnitude 21, 0.2 arcsecond astrometric accuracy at J2000, 0.3 magnitude photometric accuracy in up to five colors, and 85% accuracy for distinguishing stars from non-stellar objects. This is a large database, around 80 GB, and is not available for download, but can be searched here.
What to use?
If astrometry is important, USNO recommends that data be used in the following order (use the first, if not available in that data set go down to the next, and so on):
- Hipparcos Catalog (to about magnitude 7.3)
- UCAC2 Catalog (to about magnitude 10)
- Tycho-2 Catalog (to about magnitude 11.5)
- USNO-B Catalog (to about magnitude 21)
USNO has an excellent page here describing different star catalogs, with recommendations on which to use depending upon your application.
The UCAC2 Catalog
This is from the UCAC project, designed to map the whole sky from magnitudes 7.5 to 16. This survey is based on the USNO Twin Astrograph. The observed positional errors are about 20 milliarcseconds for the stars in the 10 to 14 magnitude range, and about 70 milliarcseconds at the limiting magnitude of 16. More information about the catalog here.
Other Specialized Catalogs
Besides these, there are other specialized catalogs which serve as databases for special objects/measurements. Some of the more popular are listed below.
Gliese Catalog: Catalog of Nearby Stars (CNS3) Listing the stars closest to Earth (within 25 parsecs).
General Catalog of Trigonometric Parallaxes: Lists about 9000 stars for which parallax measurements have been made. The Gliese catalog is actually a subset of this catalog, since it's based on parallax measurements.
Non-Star Catalogs: There are many catalogs containing non-stellar objects, such as the Messier Objects Catalog, the New General Catalog (NGC) of deep sky objects, the Caldwell Catalog, the Herschel 400 Catalog, etc.