Hail Mary is a Christian prayer to Mary, the mother of Jesus. Most of the prayer comes from the Gospel of Luke. Some things were also added to the prayer during the 13th century (the 1200s). When a person says a Hail Mary, they asks Mary to pray for them.

In Roman Catholicism, the Hail Mary makes up the most important part of the Rosary. The Eastern Orthodox and Oriental Orthodox also use the prayer. So do many other groups within Christianity, including Anglicans, Independent Catholics, and Old Catholics. Some Protestant denominations also use the Hail Mary.

Hail Mary in the Bible
The Hail Mary uses two phrases from Saint Luke's Gospel. The first is "Hail, full of grace, the Lord is with thee, blessed art thou amongst women" ().  (In Simple English, this means: "Be glad.  You are full of grace.  You are with God.  You are blessed.")  The second is "Blessed art thou amongst women and blessed is the fruit of thy womb" ().  (This means: "You and your child (Jesus) are both blessed.")

When the Hail Mary was first created, it was much shorter than it is now.  In Western Europe, in the mid-13th century, the prayer was just a few words. The word "Mary" was added after the word "Hail."  The entire prayer was "Hail Mary, full of grace." We know this from Saint Thomas Aquinas's writings about the prayer.

In the first phrase from Saint Luke's Gospel, the Angel Gabriel is greeting Mary.  Like all of Saint Luke's Gospel, this phrase was first written in Koine Greek. The first word of greeting, , chaíre, is translated "Hail."  This means "Rejoice" or "Be glad."  This was a normal greeting in Koine Greek.  These greetings are still used in modern Greek.

The prayer in Eastern (Greek) tradition
The Hail Mary prayer used by the Eastern Orthodox Church and Eastern Catholic Churches is written:  This means:
Theotokos Virgin, rejoice, Mary full of grace, the Lord is with you. Blessed are you among women, and blessed is the fruit of your womb, for you have borne the Saviour of our souls.

The same thing can be translated differently into English:

Mother of God and Virgin, rejoice, Mary full of grace, the Lord is with thee. Blessed art thou amongst women, and blessed is the fruit of thy womb, for thou hast given birth to the Saviour of our souls.

"Theotokos" is the title given to Mary in the Eastern Churches.  It is a Greek word that means "the one who gives birth to God."

The prayer in Western (Latin) tradition
There are different ideas about when the Hail Mary was changed to today's version.  The Catholic Encyclopedia says that the Hail Mary was not changed until about 1050.

Saint Thomas Aquinas said that by the mid-thirteenth century, the Western churches had added only one word - "Mary" - to the Biblical verses the prayer came from. Adding her name made it clear that Mary was the person the prayer talked to.  However, around the same time, the name "Jesus" was also added. This made it clear that Jesus was "the fruit of [Mary's] womb." 

This means that the Western version of the Hail Mary did not come from the Greek version.  The Greek version has very different words, like "for thou hast given birth to the Saviour of our souls," which never appeared in the Western version.

Before the 16th century, the Hail Mary greeted and praised Mary.  However, during the 16th century, new words were added.  These new words asked Mary for help.  In 1555, a Dutch Jesuit named Petrus Canisius added these words to his catechism: "Holy Mary, Mother of God, pray for us sinners."  By the time of the Council of Trent eleven years later, this sentence, and some new words, had been added to the Hail Mary.  In 1566, the Catechism of the Council of Trent included this sentence in the prayer: "Holy Mary, Mother of God, pray for us sinners now and at the hour of our death. Amen."

This is the last change that has been made to the Hail Mary. 

In Latin, the prayer is written this way (the macrons are given for pronunciation only and do not appear in the Latin language):

Avē Marīa, grātia plēna, Dominus tēcum. Benedicta tū in mulieribus, et benedictus frūctus ventris tuī, Iēsus.
Sancta Marīa, Māter Deī, ōrā prō nōbīs peccātōribus, nunc et in hōrā mortis nostræ. Āmēn.
Hail Mary, full of grace, the Lord is with thee; blessed art thou among women, and blessed is the fruit of thy womb, Jesus.
Holy Mary, Mother of God, pray for us sinners, now and at the hour of our death. Amen.

For translations from the Latin into various languages, see Wikisource.

The prayer in Syriac Orthodox tradition
The Syriac Orthodox Church uses a different version of the Hail Mary. This version is much closer to today's Western form than the Greek form.

In this prayer, a leader starts the prayer and everyone else says the rest:

Leader: Hail Mary, full of grace.
People: Our Lord is with Thee. Blessed art Thou among women, and blessed is the fruit of Thy womb, our Lord, Jesus Christ. O Virgin Saint Mary, O Mother of God, pray for us sinners, now and at all times, and at the hour of our death. Amen.

Usage in the Eastern Orthodox and Eastern Catholic Churches
In the Eastern Orthodox and Eastern Catholic Churches, the Hail Mary is very common.  It is said in the Greek form, or in translations from the Greek form.  The prayer is not said quite as often as in the West. However, it is well-known and is still used often.  It also appears in several canons of prayer.  It is usually sung three times at the end of Vespers during an All-Night Vigil.  It is also said many times during daily prayers.

Variant Slavonic versions
There are two different versions of the Hail Mary in Church Slavonic:

Богородице дѣво радѹйсѧ
ωбрадованнаѧ Марїе
Господь съ тобою
благословена ты въ женахъ,
и благословенъ плодъ чрева твоегω,
Якω родила еси Христа Спаса,
Избавителѧ дѹшамъ нашимъ.
Theotokos Virgin, rejoice, (or, Rejoice, O Virgin Theotokos) 
Mary full of grace,
the Lord is with thee.
Blessed art thou among women,
and blessed is the fruit of thy womb,
for thou hast borne Christ the Saviour, 
the Deliverer of our souls.

Богородице дѣво, радѹйсѧ,
Благодатнаѧ Марїе,
Господь съ тобою:
благословена Ты въ женахъ,
и благословенъ плодъ чрева Твоегω;
якω Спаса родила еси дѹшъ нашихъ.
Theotokos Virgin, rejoice,  (or, Rejoice, O Virgin Theotokos)
Mary full of grace,
The Lord is with thee.
Blessed art thou among women,
and blessed is the fruit of thy womb,
for thou hast borne the Saviour of our souls.

The first version is older.  The Old Believers still use this version.  So do the Ukrainian Greek-Catholic Church and the Ruthenian Catholic Church. 

The second version was created in 1656, as part of changes to liturgy made by Patriarch Nikon of Moscow. This version is used by the Russian Orthodox Church, the Serbian Orthodox Church, the Bulgarian Orthodox Church, and the Ukrainian Orthodox Church.

Usage in the Roman Catholic Church

The Hail Mary is the most important part of the Rosary.  The Rosary is a way of praying. It is often used by Latin Rite (Western) Catholics. It is also used in the East (but only by Latinised Ukrainian and Maronite Catholics). 

When praying the Rosary, Catholics pray ten sets of Hail Marys.  Before each set, they pray one Our Father (also called the Pater Noster or The Lord's Prayer).  After each set of Hail Marys, they pray one 'Glory Be' (Gloria Patri).  One set of these prayers is called a "decade."  Usually, Catholics say five decades when they pray the Rosary.

While praying each decade, Catholics think about the four different Mysteries of the Rosary.  Each of the Mysteries has to do with things that happened in Jesus' and Mary's lives.  The Mysteries include:
 Things that happened during Jesus's childhood (Joyful Mysteries)
 Jesus' public ministry (Luminous Mysteries)
 The Passion, including Jesus' crucifixion (Sorrowful Mysteries)
 Jesus' Resurrection onwards (Glorious Mysteries)
The Hail Mary is also the most important part of the Angelus. This is a prayer that many Catholics say three times every day. Some Anglicans and Lutherans say the Angelus too.

Anglican use of the Hail Mary
Traditional Anglicans also use the Hail Mary, in mostly the same way as Roman Catholics do.  Both groups use the Rosary and say the Angelus.  Anglican churches often have statues of the Virgin Mary. 

Many Anglicans pray the Hail Mary.  However, in different areas, the prayer may be used differently. This is because the Catholic and Anglican Churches have some different beliefs.

Musical settings 
Many people have written music for the Hail Mary (also called the Ave Maria).

During the Renaissance 
During the Renaissance, the Hail Mary very often set to music by composers, like Jacques Arcadelt, Josquin Desprez, Orlando di Lasso, and Giovanni Pierluigi da Palestrina.  However, at this time (before the Council of Trent), there were still different versions of the prayer. Because of this, some of the earlier Renaissance pieces have different words than today's Hail Mary.  For example, Josquin Desprez actually created more than one musical version of the Ave Maria.

Later versions 
One of the most famous musical versions of the prayer was created by Charles Gounod in 1859.  He added melody and words to Johann Sebastian Bach's first prelude (the beginning piece of music) from The Well-Tempered Clavier.

Other famous musical versions of the Hail Mary were written by:
 Antonín Dvořák in 1877
 Giuseppe Verdi, a famous composer, in 1887 (for his opera Otello)
 César Cui, a Russian composer.  He set the Hail Mary to music at least three different times.  First he wrote the Ave Maria in 1886.  He also used the prayer as part of two of his operas: Le Flibustier (1894) and Mateo Falcone (1907).  
 Famous composers including Mozart, Byrd, Elgar, Verdi, Saint-Saens, Rossini, Brahms and Perosi
 Famous Eastern European composers - including Rachmaninov, Stravinsky, and Bortniansky - who wrote musical versions of the Hail Mary in Slavonic

In Protestantism

Protestant Christianity does not venerate Mary.  Some Protestants have used musical versions of the Ave Maria, but changed the words.  For example, Ave Redemptor uses the music of the Ave Maria, but focuses on Jesus instead:

Ave redemptor, Domine Jesus:
Cujus ob opus
Superatur mors, enim salvatio
Nunc inundavit super universam terram.

Sancte redemptor, reputata
Fides est nobis peccatoribus,
Nunc et in morte, ad iustitiam.ENGLISH TRANSLATION
Hail the Redeemer, Lord Jesus,
By whose work
Death is defeated, for salvation
Has now overflowed upon all of the world.

Holy redeemer, our faith
Is reckoned to us sinners,
Now and in death, as righteousness.

References

Other websites 
The prayer on roman-catholic-prayers.com 
Ave Maria on video/audio sung by Sharon Janis 
Catholic Encyclopedia 1910: Hail Mary
Brief commentary on the Hail Mary from the Catechism of the Catholic Church
Ave Maria  article in Christian Cyclopedia
Various Ave Maria hymn  Ave Maria(MIDI by JE1EMU)
Text of the Hail Mary in many foreign languages
http://www.ewtn.org

Christian prayers
Mary (mother of Jesus)