Mythology and origins
Alcyone in classical Greek mythology was one of the Pleiades, the "seven sisters". The seven sisters were the daughters of Atlas (one of the Titans) and Pleione (a Nymph). The seven sisters were named Alcyone, Maya, Asterope, Merope, Electra, Taygeta and Celaeno. Alcyone had a son, Hyrieus, by Poseidon, God of the sea. Poseidon was also called Neptunus (Neptune) by the Romans.
"The Pleiades" by Elihu Vedder (1885) - public domain image.
Another Alcyone occurs in some ancient Greek myths. She was the daughter of Aeolus, "Ruler of the Winds", and Enarete.  In this myth, she was married to Ceyx - and they were so enthralled with their union that they dared to called themselves Zeus and Hera - for which presumption, Zeus turned them into birds. In another version of the story, Ceyx perished in a shipwreck and Alcyone threw herself into the sea, before both were turned into birds by the Gods, out of compassion.
Alcyone in astronomy
Alcyone is the "central" (as appears from Earth) and brightest star of the Pleiades - an "open cluster" of blue-white stars in the constellation of Taurus. Alcyone, or Eta Tauri, is a "blue giant" star classified as having the spectral type B7IIIe. Alcyone is estimated by Burnham to have 1000 times the luminosity of the sun and 20 times its diameter.  Alcyone is estimated to be 368 (plus or minus 41) light years from Earth and have an Apparent Magnitude of 2.85. 
Blue stars are relatively "young" in stellar terms. According to astronomers, stars gradually cool as they age, turning yellow, then red.
The Pleiades star cluster actually contains many stars, estimated to be several hundred, as may be seen with a powerful telescope; but according to  there are nine "blue giants". Around seven are generally visible to the naked eye - hence the name "seven sisters" - although some people with very good eyesight are said to be able to pick out up to a dozen stars in the pleiades unaided. Stargazing is best accomplished at or around the time of the new moon and away from towns and cities - because the stars can be seen with greater clarity when there is less other light around. The stars in the cluster are all within around 20 light years of each other. According to , the Bright Star Catalog indicates that Alcyone may be part of a "multiple star system' with as many as 5 other stars.
Alcyone in modern alternative spirituality
Alcyone occupies a curious place in modern mythology and "alternative" spiritual belief. Barbara Hand Clow's well known 1995 book "The Pleiadean Agenda"  depicts one "Satya of Alcyone", a cosmic being with a message for humanity. 
The star Alcyone is said to have been revered by the ancient Mayans as the home of their ancestors. In Barbara Hand Clow's book, the "voice" of Satya states that the Maya of ancient Central America originated from the "Timekeepers", also called Maya, a group of beings from a star near Alcyone. 
Some sources even believe that Alcyone is half way between the Pleiades and the Solar System, with both systems revolving around Alcyone! Regardless of how unlikely this may be, it is interesting to note that for some unknown region, Alcyone finds itself at the centre of some interesting and unusual tales - and it seems to find itself surrounded by an unusual amount of mystique, with perhaps only Sirius having greater reputation in this regard.
Alcyone in the arts and popular culture
Perhaps for these reasons, or perhaps for some more mysterious reason, artists, writers and musicians have been drawn to Alcyone in greater numbers than to many other stars. Here is a list of musicians who have adopted the name:
Alcyone Prophet Electronic music artist (Trance / Techno) from Kansas, USA.
Alcyone Live electronic music act featuring Alex Alcyone and Suzanne Sterling, based in California, USA.
Alex Alcyone Electronic music artist, writer and creator of this page.
Alcyon Massive Reggae artist / live act from Oregon, USA.
Alcyone was also another name adopted by the famous spiritual teacher Krishnamurti. Krishnamurti, born in India, famously said "Truth is a pathless land"  and wrote several books about enlightenment.
The Cousteau Society, founded in 1973 by Captain Jacques-Yves Cousteau, named their expedition ship Alcyone. Designed to run with an advanced "mixed propulsion' system, Alcyone has travelled all over the world studying marine wildlife.
Alcyone has also been a name used by businesses from Apartment complexes through to Software companies.
The motor company Subaru named one of their cars Alcyone. The name Subaru in Japanese means Pleiades and the Subaru corporate logo can bee seen to contain the stars - presumably with Alcyone as the bright one!
Astrology / Ancient Comsology
In astrology, the star Alcyone, moving at one degree every 72 years due to precession of the equinoxes, is currently at around 0 degrees Gemini. It was at at 29º36 Taurus in 1971.
On May 20th 2012, A solar eclipse will occur in direct alignment with Alcyone and the Pleiades.  Believers of the "Mayan Prophecy" myths and followers of the Mayan Calendar think that 2012 is the beginning of a new era, and that this eclipse is an event of cosmic significance.
It's said that the Maya werenot the only ones who held Alcyone to be of great significance. The Dogon  of Africa, and also the Egyptians may have done so. Joseph Augustus Seiss, in his 1877 book "A miracle in stone, or, The great pyramid of Egypt", makes this interesting statement:
"It is by means of this cycle [i.e. the precession of the equinoxes], in connection with its star-pointings, that the Great Pyramid also tells the date of its erection. Sir John Herschel in 1839, assuming that its long, narrow, polished tubular entrance passage was meant to be levelled at a polar star, began to calculate back with what data he had to find the time when such a star was looking down that tube from the northern heavens. Nor did he fail to find one answering the conditions near about the time assigned by other methods as the probable date at which the Great Pyramid was built. Closer determinations of the exact pointings of the grand tube, along with other data, enabled other astronomers to repeat the calculation with more determinate results, fixing upon the year two thousand one hundred and seventy before Christ, as that in which this tube pointed to a Draconis, the then pole star, at its lower culmination, at the same time that the Pleiades, particularly Alcyone, the centre of the group, were on the same meridian above. And as this was a mark in the heavens which could not occur again for more than twenty-five thousand years from that time, and was itself very extraordinary, it has been accepted as meant to be the sign of the date of the building of the Great Pyramid.
...Science has at last discovered that the sun is not a dead centre, with planets and comets wheeling about it but itself stationary. It is now ascertained that the sun also is in motion, carrying with it its splendid retinue of comets, planets, its satellites and theirs, around some other and vastly mightier centre. Astronomers are not yetfully agreed as towhatorwhere that centre is. Some, however, believe that they have found the direction of it to be the Pleiades, and particularly Alcyone, the central one of the renowned Pleiadic stars. To the distinguished German astronomer, Prof. J. H. Maedler, belongs the honor of having made this discovery." 
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 Seiss, Joseph A. Miracle in Stone: or the Great Pyramid of Egypt - available at http://books.google.com/books?id=NUsWAAAAYAAJ
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